We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectly conducting conditions on the magnetic field in a smooth bounded domain Ω ⊂ ℝ3. It is shown that there exists a unique strong solution to the incompressible viscous magnetohydrodynamic

This paper is devoted to studying the zero dissipation limit problem for the one-dimensional compressible Navier-Stokes equations with selected density-dependent viscosity. In particular, we focus our attention on the viscosity taking the form μ(ρ) = ρϵ(ϵ > 0). For the selected density-dependent viscosity, it is proved that the solutions of the one-dimensional compressible Navier-Stokes equations with

In this paper, we give some rigidity results for complete self-shrinking surfaces properly immersed in ℝ4 under some assumptions regarding their Gauss images. More precisely, we prove that this has to be a plane, provided that the images of either Gauss map projection lies in an open hemisphere or \({{\mathbb{S}}^2}(1/\sqrt 2 )\backslash \bar {\mathbb{S}}_ + ^1(1/\sqrt 2 )\). We also give the classification

In this paper, we prove the uniqueness of the Lp Minkowski problem for q-torsional rigidity with p > 1 and q > 1 in smooth case. Meanwhile, the Lp Brunn-Minkowski inequality and the Lp Hadamard variational formula for q-torsional rigidity are established.

In this paper, we propose an iterative algorithm to find the optimal incentive mechanism for the principal-agent problem under moral hazard where the number of agent action profiles is infinite, and where there are an infinite number of results that can be observed by the principal. This principal-agent problem has an infinite number of incentive-compatibility constraints, and we transform it into

In this article, several theorems of fractional conformable derivatives and triple Sumudu transform are given and proved. Based on these theorems, a new conformable triple Sumudu decomposition method (CTSDM) is intrduced for the solution of singular two-dimensional conformable functional Burger’s equation. This method is a combination of the decomposition method (DM) and Conformable triple Sumudu transform

In this paper, we establish some oscillation criteria for higher order nonlinear delay dynamic equations of the form $${[{r_n}\varphi {( \cdots {r_2}{({r_1}{x^\Delta })^\Delta } \cdots )^\Delta }]^\Delta }(t) + h(t)f(x(\tau (t))) = 0$$ on an arbitrary time scale \(\mathbb{T}\) with sup \(\mathbb{T} = \infty \), where n ≥ 2, φ(u) = ∣u∣γsgn(u) for γ > 0, ri(1 ≤ i ≤ n) are positive rd-continuous functions

We consider a nonlinear Dirichlet problem driven by a (p, q)-Laplace differential operator (1 < q < p). The reaction is (p − 1)-linear near ±∞ and the problem is noncoercive. Using variational tools and truncation and comparison techniques together with critical groups, we produce five nontrivial smooth solutions all with sign information and ordered. In the particular case when q = 2, we produce a

There is little work concerning the properties of quaternionic operators acting on slice regular function spaces defined on quaternions. In this paper, we present an equivalent characterization for the boundedness of the product operator CϕDm acting on Bloch-type spaces of slice regular functions. After that, an equivalent estimation for its essential norm is established, which can imply several existing

The precise Lp norm of a class of Forelli-Rudin type operators on the Siegel upper half space is given in this paper. The main result not only implies the upper Lp norm estimate of the Bergman projection, but also implies the precise Lp norm of the Berezin transform.

In this paper, we derive some \(\partial \overline \partial \)-Bochner formulas for holomorphic maps between Hermitian manifolds. As applications, we prove some Schwarz lemma type estimates, and some rigidity and degeneracy theorems. For instance, we show that there is no non-constant holomorphic map from a compact Hermitian manifold with positive (resp. non-negative) ℓ-second Ricci curvature to a

We prove the global existence and exponential decay of strong solutions to the three-dimensional nonhomogeneous asymmetric fluid equations with nonnegative density provided that the initial total energy is suitably small. Note that although the system degenerates near vacuum, there is no need to require compatibility conditions for the initial data via time-weighted techniques.

In this paper, we will study the nonlocal and nonvariational elliptic problem $$\left\{ {\matrix{{ - (1 + a\|u\|_q^{\alpha q})\Delta u = |u{|^{p - 1}}u + h(x,u,\nabla u)\,{\rm{in}}\,\,\,\Omega ,} \hfill \cr {u = 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,on\,\,\,\partial \Omega ,} \hfill

This paper investigates the nonemptiness and compactness of the mild solution set for a class of Riemann-Liouville fractional delay differential variational inequalities, which are formulated by a Riemann-Liouville fractional delay evolution equation and a variational inequality. Our approach is based on the resolvent technique and a generalization of strongly continuous semigroups combined with Schauder’s

Nonlinear delay Caputo fractional differential equations with non-instantaneous impulses are studied and we consider the general case of delay, depending on both the time and the state variable. The case when the lower limit of the Caputo fractional derivative is fixed at the initial time, and the case when the lower limit of the fractional derivative is changed at the end of each interval of action

Assume that X and Y are real Banach spaces with the same finite dimension. In this paper we show that if a standard coarse isometry f: X → Y satisfies an integral convergence condition or weak stability on a basis, then there exists a surjective linear isometry U: X → Y such that ‖f (x) − Ux‖ = o(‖x‖) as ‖x‖ → ∞. This is a generalization about the result of Lindenstrauss and Szankowski on the same

We investigate the Hyers—Ulam stability (HUS) of certain second-order linear constant coefficient dynamic equations on time scales, building on recent results for first-order constant coefficient time-scale equations. In particular, for the case where the roots of the characteristic equation are non-zero real numbers that are positively regressive on the time scale, we establish that the best HUS constant

The main purpose of this paper is to extend the Zolotarev’s problem concerning with geometric random sums to negative binomial random sums of independent identically distributed random variables. This extension is equivalent to describing all negative binomial infinitely divisible random variables and related results. Using Trotter-operator technique together with Zolotarev-distance’s ideality, some

In this paper, we prove the existence of positive solutions to the following weighted fractional system involving distinct weighted fractional Laplacians with gradient terms $$\left\{ {\matrix{{( - \Delta )_{{a_1}}^{{\alpha \over 2}}{u_1}(x) = u_1^{{q_{11}}}(x) + u_2^{{q_{12}}}(x) + {h_1}(x,{u_1}(x),{u_2}(x),\nabla {u_1}(x),\nabla {u_2}(x)),\,\,\,\,\,\,x \in \Omega ,} \hfill \cr {( - \Delta )_{{a_2}}^{{\beta

In this paper, we apply Fokas unified method to study the initial boundary value (IBV) problems for nonlinear integrable equation with 3 × 3 Lax pair on the finite interval [0, L]. The solution can be expressed by the solution of a 3 × 3 Riemann-Hilbert (RH) problem. The relevant jump matrices are written in terms of matrix-value spectral functions s(k), S(k), Sl(k), which are determined by initial

In this paper, we study the existence of nontrivial solutions to the elliptic system $$\left\{ {\begin{array}{*{20}{c}} { - \Delta u = \lambda v + {F_u}(x,u,v),}&{x \in \Omega \;} \\ { - \Delta v = \lambda u + {F_v}(x,u,v),}&{x \in \Omega \;} \\ {u = u = 0,\;\;\;\;\;\;\;\;\;\;\;\;\;\;}&{x \in \partial \Omega } \end{array}} \right.$$ where Ω ⊂ ℝN is bounded with a smooth boundary. By the Morse theory

For entire or meromorphic function f, a value θ ∈ [0, 2π) is called a Julia limiting direction if there is an unbounded sequence {zn} in the Julia set satisfying \(\mathop {\lim }\limits_{n \to \infty } \;\arg {z_n} = \theta \). Our main result is on the entire solution f of P(z, f) + F(z)fs = 0, where P(z, f) is a differential polynomial of f with entire coefficients of growth smaller than that of

In this paper we consider a class of polynomial planar system with two small parameters, ε and λ, satisfying 0 < ε ≪ λ ≪ 1. The corresponding first order Melnikov function M1 with respect to ε depends on λ so that it has an expansion of the form \({M_1}(h,\lambda ) = \sum\limits_{k = 0}^\infty {{M_{1k}}(h){\lambda ^k}} \). Assume that M1k′ (h) is the first non-zero coefficient in the expansion. Then

In this paper, we consider the following new Kirchhoff-type equations involving the fractional p-Laplacian and Hardy-Littlewood-Sobolev critical nonlinearity: $$\begin{array}{*{20}{c}} {{{\left( {a + b\iint_{{\mathbb{R}^N}} {\frac{{{{\left| {u(x) - u(y)} \right|}^p}}}{{{{\left| {x - y} \right|}^{N + ps}}}}\text{d}x\text{d}y}} \right)}^{p - 1}}}&{( - \Delta )_p^su + \lambda V(x){{\left| u \right|}^{p

In this paper, we construct k-valued random analytic algebroid functions for the first time. By combining the properties of random series, we study the growth and Borel points of random analytic algebroid functions in the unit disc and obtain some interesting theorems.

In this article, we propose a new algorithm and prove that the sequence generalized by the algorithm converges strongly to a common element of the set of fixed points for a quasi-pseudo-contractive mapping and a demi-contraction mapping and the set of zeros of monotone inclusion problems on Hadamard manifolds. As applications, we use our results to study the minimization problems and equilibrium problems

Given n ≥ 2 and \(\alpha > \tfrac{1}{2}\), we obtained an improved upbound of Hausdorff’s dimension of the fractional Schrödinger operator; that is, $$\mathop {\sup }\limits_{f \in {H^s}({\mathbb{R}^n})} {\dim _H}\left\{ {x \in {{\mathbb{R}^n}}:\;\mathop {\lim }\limits_{t \to 0} {e^{{\rm{i}}t{{( - \Delta )}^\alpha }}}f(x) \ne f(x)} \right\} \le n + 1 - {{2(n + 1)s} \over n}$$ for \(\tfrac{n}{{2(n +

The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary conditions described by a combination of the Signorini unilateral frictionless contact condition, and nonmonotone multivalued contact, and friction laws of subdifferential form. First, under suitable assumptions, we deliver the weak formulation of the contact

Some sufficient conditions of the energy conservation for weak solutions of incompressible viscoelastic flows are given in this paper. First, for a periodic domain in ℝ3, and the coefficient of viscosity μ = 0, energy conservation is proved for u and F in certain Besov spaces. Furthermore, in the whole space ℝ3, it is shown that the conditions on the velocity u and the deformation tensor F can be relaxed

We establish a slow manifold for a fast-slow dynamical system with anomalous diffusion, where both fast and slow components are influenced by white noise. Furthermore, we verify the exponential tracking property for the established random slow manifold, which leads to a lower dimensional reduced system. Alongside this we consider a parameter estimation method for a nonlocal fast-slow stochastic dynamical

We study the regularity of weak solutions to a class of second order parabolic system under only the assumption of continuous coefficients. We prove that the weak solution u to such system is locally Hölder continuous with any exponent α ∈ (0, 1) outside a singular set with zero parabolic measure. In particular, we prove that the regularity point in QT is an open set with full measure, and we obtain

We investigate the asymptotic behavior of solutions to the initial boundary value problem for the micropolar fluid model in a half line ℝ+ ≔ (0, ∞). Inspired by the relationship between a micropolar fluid model and Navier-Stokes equations, we prove that the composite wave consisting of the transonic boundary layer solution, the 1-rarefaction wave, the viscous 2-contact wave and the 3-rarefaction wave

In this paper, we propose a new method, called the level-collapsing method, to construct branching Latin hypercube designs (BLHDs). The obtained design has a sliced structure in the third part, that is, the part for the shared factors, which is desirable for the qualitative branching factors. The construction method is easy to implement, and (near) orthogonality can be achieved in the obtained BLHDs

We are concerned with the shock diffraction configuration for isothermal gas modeled by the conservation laws of nonlinear wave system. We reformulate the shock diffraction problem into a linear degenerate elliptic equation in a fixed bounded domain. The degeneracy is of Keldysh type—the derivative of a solution blows up at the boundary. We establish the global existence of solutions and prove the

Boyd’s interpolation theorem for quasilinear operators is generalized in this paper, which gives a generalization for both the Marcinkiewicz interpolation theorem and Boyd’s interpolation theorem. By using this new interpolation theorem, we study the spherical fractional maximal functions and the fractional maximal commutators on rearrangement-invariant quasi-Banach function spaces. In particular,

In this paper, we consider a delayed diffusive SVEIR model with general incidence. We first establish the threshold dynamics of this model. Using a Nonstandard Finite Difference (NSFD) scheme, we then give the discretization of the continuous model. Applying Lyapunov functions, global stability of the equilibria are established. Numerical simulations are presented to validate the obtained results.

By applying the standard fixed point theorems, we prove the existence and uniqueness results for a system of coupled differential equations involving both left Caputo and right Riemann-Liouville fractional derivatives and mixed fractional integrals, supplemented with nonlocal coupled fractional integral boundary conditions. An example is also constructed for the illustration of the obtained results

Let 0 < α, β < n and f, g ∈ C([0, ∞) × [0, ∞)) be two nonnegative functions. We study nonnegative classical solutions of the system $$\left\{ {\begin{array}{*{20}{c}} {{{( - \Delta )}^{\tfrac{\alpha }{2}}}u = f(u,v)}&{\text{in}\;{\mathbb{R}^n},} \\ {{{( - \Delta )}^{\tfrac{\beta }{2}}}v = g(u,v)}&{\text{in}\;{\mathbb{R}^n},} \end{array}} \right.$$ and the corresponding equivalent integral system. We

This paper is concerned with a stability problem on perturbations near a physically important steady state solution of the 3D MHD system. We obtain three major results. The first assesses the existence of global solutions with small initial data. Second, we derive the temporal decay estimate of the solution in the L2-norm, where to prove the result, we need to overcome the difficulty caused by the

This paper is concerned with the spatial propagation of an SIR epidemic model with nonlocal diffusion and free boundaries describing the evolution of a disease. This model can be viewed as a nonlocal version of the free boundary problem studied by Kim et al. (An SIR epidemic model with free boundary. Nonlinear Anal RWA, 2013, 14: 1992–2001). We first prove that this problem has a unique solution defined

In this article, we study the exhaustive analysis of nonlinear wave interactions for a 2 × 2 homogeneous system of quasilinear hyperbolic partial differential equations (PDEs) governing the macroscopic production. We use the hodograph transformation and differential constraints technique to obtain the exact solution of governing equations. Furthermore, we study the interaction between simple waves

In this article, we present the existence, uniqueness, Ulam-Hyers stability and Ulam-Hyers-Rassias stability of semilinear nonautonomous integral causal evolution impulsive integro-delay dynamic systems on time scales, with the help of a fixed point approach. We use Grönwall’s inequality on time scales, an abstract Gröwall’s lemma and a Picard operator as basic tools to develop our main results. To

We prove that, as in the finite dimensional case, the space of Bloch functions on the unit ball of a Hilbert space contains, under very mild conditions, any semi-Banach space of analytic functions invariant under automorphisms. The multipliers for such Bloch space are characterized and some of their spectral properties are described.

In this paper, we consider a class of left invariant Riemannian metrics on Sp(n), which is invariant under the adjoint action of the subgroup Sp(n − 3) × Sp(1) × Sp(1) × Sp(1). Based on the related formulae in the literature, we show that the existence of Einstein metrics is equivalent to the existence of solutions of some homogeneous Einstein equations. Then we use a technique of the Gröbner basis

In this paper, dynamics analysis of a delayed HIV infection model with CTL immune response and antibody immune response is investigated. The model involves the concentrations of uninfected cells, infected cells, free virus, CTL response cells, and antibody antibody response cells. There are three delays in the model: the intracellular delay, virus replication delay and the antibody delay. The basic

In this paper, we establish the global existence and uniqueness of the solution of the Cauchy problem of a one-dimensional compressible isentropic Euler system for a Chaplygin gas with large initial data in the space L 1loc . The hypotheses on the initial data may be the least requirement to ensure the existence of a weak solution in the Lebesgue measurable sense. The novelty and also the essence of

We consider Toeplitz operators Tu with symbol u on the Bergman space of the unit ball, and then study the convergences and summability for the sequences of powers of Toeplitz operators. We first charactreize analytic symbols φ for which the sequence \(T_\varphi ^{*k}\) f or \(T_\varphi ^k\) f converges to 0 or ∞ as k → ∞ in norm for every nonzero Bergman function f. Also, we characterize analytic symbols

Let f be a twice continuously differentiable self-mapping of a unit disk satisfying Poisson differential inequality ∣Δf(z)∣ ≤ B · ∣Df (z)∣2 for some B > 0 and f(0) = 0. In this note, we show that f does not always satisfy the Schwarz-Pick type inequality $$\frac{1-\vert z\vert^{2}}{1-\vert f(z)\vert^{2}}\leq\ C(B),$$ where C(B) is a constant depending only on B. Moreover, a more general Schwarz-Pick

In the article, we prove that the double inequalities $$\begin{array}{*{20}{c}} {{G^p}\left[ {{\lambda _1}a + \left( {1 - {\lambda _1}} \right)b,{\lambda _1}b + \left( {1 - {\lambda _1}} \right)a} \right]{A^{1 - p}}\left( {a,b} \right) < T\left[ {A\left( {a,b} \right),G\left( {a,b} \right)} \right]} \\ { < {G^p}\left[ {\mu _1^{}a + \left( {1 - {\mu _1}} \right)a} \right]{A^{1 - p}}\left( {a,b} \right)

For n ≥ 3, we construct a class \(\left\{{{W_{n,{\pi _1},{\pi _2}}}} \right\}\) of n2 × n2 hermitian matrices by the permutation pairs and show that, for a pair {π1, π2} of permutations on (1, 2, …, n), \({{W_{n,{\pi _1},{\pi _2}}}}\) is an entanglement witness of the n ⊗ n system if {π1, π2} has the property (C). Recall that a pair {π1, π2} of permutations of (1, 2, …, n) has the property (C) if,

We are concerned with the nonlinear Schrödinger-Poisson equation $$\begin{cases}-\Delta u+(V(x)-\lambda)u+\phi(x)u=f(u),\\-\Delta\phi=u^{2},\lim\limits_{\vert x\vert\rightarrow+\infty}\phi(x)=0,x\in \mathbb{R}^{3},\end{cases}\ {\mathrm{(P)}}$$ where λ is a parameter, V (x) is an unbounded potential and f (u) is a general nonlinearity. We prove the existence of a ground state solution and multiple solutions

This article proposes a high-order numerical method for a space distributed-order time-fractional diffusion equation. First, we use the mid-point quadrature rule to transform the space distributed-order term into multi-term fractional derivatives. Second, based on the piecewise-quadratic polynomials, we construct the nodal basis functions, and then discretize the multi-term fractional equation by the

Denote a finite dimensional Hopf C*-algebra by H, and a Hopf *-subalgebra of H by H1. In this paper, we study the construction of the field algebra in Hopf spin models determined by H1 together with its symmetry. More precisely, we consider the quantum double D(H, H1) as the bicrossed product of the opposite dual \(\widehat{{H^{op}}}\) of H and H1 with respect to the coadjoint representation, the latter

The severe acute respiratory syndrome COVID-19 was discovered on December 31, 2019 in China. Subsequently, many COVID-19 cases were reported in many other countries. However, some positive COVID-19 samples had been reported earlier than those officially accepted by health authorities in other countries, such as France and Italy. Thus, it is of great importance to determine the place where SARS-CoV-2

In this paper, we give a characterization for the general complex (α, β) metrics to be strongly convex. As an application, we show that the well-known complex Randers metrics are strongly convex complex Finsler metrics, whereas the complex Kropina metrics are only strongly pseudoconvex.

The reflection of a weak shock wave is considered using a shock polar. We present a sufficient condition under which the von Neumann paradox appears for the Euler equations. In an attempt to resolve the von Neumann paradox for the Euler equations, two new types of reflection configuration, one called the von Neumann reflection (vNR) and the other called the Guderley reflection (GR), are observed in

In this paper, we study the proximal relation, regionally proximal relation and Banach proximal relation of a topological dynamical system for amenable group actions. A useful tool is the support of a topological dynamical system which is used to study the structure of the Banach proximal relation, and we prove that above three relations all coincide on a Banach mean equicontinuous system generated

This paper is concerned with the Fisher-KPP equation with diffusion and nonlocal delay. Firstly, we establish the global existence and uniform boundedness of solutions to the Cauchy problem. Then, we establish the spreading speed for the solutions with compactly supported initial data. Finally, we investigate the long time behavior of solutions by numerical simulations.

As we know, thus far, there has appeared no definition of bilinear spectral multipliers on Heisenberg groups. In this article, we present one reasonable definition of bilinear spectral multipliers on Heisenberg groups and investigate its boundedness. We find some restrained conditions to separately ensure its boundedness from \({{\cal C}_0}\left({{\mathbb{H}^n}} \right) \times {L^2}\left({{\mathbb{H}^n}}

In this paper, we consider the measure determined by a fractional Ornstein-Uhlenbeck process. For such a measure, we establish an explicit form of the martingale representation theorem and consequently obtain an explicit form of the Logarithmic-Sobolev inequality. To this end, we also present the integration by parts formula for such a measure, which is obtained via its pull back formula and the Bismut