A background to the constitutive modeling of elastic-inelastic material response is provided to highlight the uniqueness of the Eulerian formulation of general nonlinear fully anisotropic thermoelastic-inelastic materials proposed in Rubin (1994) [1]. This model introduced Eulerian evolution equations for a triad of microstructural vectors that characterize elastic deformations and anisotropic orientations

We consider an elliptic variational-hemivariational inequality 𝓟 in a reflexive Banach space, governed by a set of constraints K, a nonlinear operator A, and an element f. We associate to this inequality a sequence {𝓟n} of variational-hemivariational inequalities such that, for each n ∈ ℕ, inequality 𝓟n is obtained by perturbing the data K and A and, moreover, it contains an additional term governed

We refine a recent result on the structure of measures satisfying a linear partial differential equation 𝓐μ = σ, μ, σ are Radon measures, considering the measure μ(x) = g(x)dx + μus(x̃)(μs(x̄) + dx̄) where x = (x̃,x̄) ∈ ℝk × ℝd−k, μus is a uniformly singular measure in x̃0 and the measure μs is a singular measure. We proved that for μus-a.e. x̃0 the range of the Radon-Nykodim derivative f~(x~0)=dμusd|μus|(x~0)

No abstract is available for this article.

Mining backfill is commonly used in underground mines. A critical concern of this practice is to evaluate the pressures and total stresses in backfilled stopes to ensure a safe and economic design of barricades, constructed to retain the backfill. When a slurried backfill is placed in a mine stope, excess pore water pressure (PWP) can instantaneously generate and progressively dissipate. The dissipation

Seepage‐stress coupling is a key problem in the field of geotechnical engineering, and the finite element method is one of the main methods to study seepage‐stress coupling in rock masses. However, the finite element method has issues of poor stability, low efficiency, and low accuracy in the simulation of the seepage‐stress coupling problem. In this paper, the homogeneous saturated rock mass is taken

This paper investigates tunnel face stability in soft rock masses via coupled limit and reliability analyses. Specifically, a 3D face collapse mechanism was first constructed. Then the Hoek–Brown failure criterion was introduced into the limit analysis via the tangential technique. Taking the variability of rock mass parameters and loads into consideration, a reliability model was established. The

In this note, we investigate stability issues for a mixture of two elastic solids. The governing equations consist of two coupled systems of elastodynamic equations with a weak damping. The damping involves the difference of velocities, so that the damping operator is degenerate. First, we show that the underlying semigroup is strongly stable under a weaker parameters constraint, thereby improving

Recently, Liao and Rams [1] considered certain infinite iterated function systems that are natural generalizations of Gauss map. They studied the increasing rate of Birkhoff sums in such systems with polynomial decay of the derivative and calculated the Hausdorff dimensions of the sets of points whose Birkhoff sums share the same increasing rate for different unbounded potential functions. In this

Ground-borne vibrations are disturbing to human beings. In order to model and reduce these vibrations, the calculation of the harmonic Green's-functions of the soil is highly required since the most effective numerical solution to predict ground-borne vibration is to couple the finite-element and the boundary-element methods. In this work, we elaborate a direct space-frequency formulation that is especially

SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3131-3148, January 2020. The Cauchy problem for the Yang--Mills system in three space dimensions with data in Fourier--Lebesgue spaces $\widehat{H}^{s,r}$ , $1 < r \le 2$ , is shown to be locally well-posed, where we have to assume only almost optimal minimal regularity for the data with respect to scaling as $r \to 1$ . This is true despite

The aim of this paper is to study the stochastic SIR equation with general incidence functional responses and in which both natural death rates and the incidence rate are perturbed by white noises. We derive a sufficient and almost necessary condition for the extinction and permanence for SIR epidemic system with multi noises{dS(t)=[a1−b1S(t)−I(t)f(S(t),I(t))]dt+σ1S(t)dB1(t)−I(t)g(S(t),I(t))dB3(t)

Starting from an age-structured diffusive population growth law for single species in a discrete and periodic habitat, we formulate a stage structured population model with spatially periodic dispersal, mortality and recruitment. With a KPP type setting, after establishing the fundamental solution of a discretized heat equation with spatially periodic dispersal, we apply some recently developed dynamical

Maximum Principles on unbounded domains play a crucial rôle in several problems related to linear second-order PDEs of elliptic and parabolic type. In this paper we consider a class of sub-elliptic operators L in RN and we establish some criteria for an unbounded open set to be a Maximum Principle set for L. We extend some classical results related to the Laplacian (by Deny, Hayman and Kennedy) and

In this work we prove local existence of strong solutions to the initial-value problem arising in one-dimensional strain-limiting viscoelasticity, which is based on a nonlinear constitutive relation between the linearized strain, the rate of change of the linearized strain and the stress. The model is a generalization of the nonlinear Kelvin-Voigt viscoelastic solid under the assumption that the strain

We present a fast method for evaluating expressions of the formuj=∑i=1,i≠jnαixi−xj,forj=1,…,n, where αi are real numbers, and xi are points in a compact interval of R. This expression can be viewed as representing the electrostatic potential generated by charges on a line in R3. While fast algorithms for computing the electrostatic potential of general distributions of charges in R3 exist, in a number

The main purpose of this paper is to study higher-order sensitivity analysis in parametric vector optimization problems. Firstly, the higher-order proto-differentiability/the higher-order asymptotic proto-differentiability of the feasible map of a parametric vector optimization problem are considered. Then, we verify that the weak efficient solution map and the weak perturbation map of a parameterized

The present paper is devoted to the study of backward stochastic differential equations driven by G-Brownian motion (G-BSDEs) with time-varying Lipschitz condition. With the help of nonlinear stochastic analysis technique and approximation method, we prove that the G-BSDEs admit a unique solution on finite or infinite time horizon. Furthermore, we obtain the corresponding comparison theorem.

For 0

The deformability condition for submanifolds of fixed degree immersed in a graded manifold can be expressed as a system of first order PDEs. In the particular but important case of ruled submanifolds, we introduce a natural choice of coordinates, which allows to deeply simplify the formal expression of the system, and to reduce it to a system of ODEs along a characteristic direction. We introduce a

We study Hausdorff convergence (and related topics) in the chordalization of a metric space to better understand pointed Gromov-Hausdorff convergence of quasihyperbolic distances (and other conformal distances).

In this paper, we prove a global Calderón-Zygmund type estimate in the framework of Lorentz spaces for a variable power of the gradients to the zero-Dirichlet problem of general nonlinear elliptic equations with the nonlinearities satisfying Orlicz growth. It is mainly assumed that the variable exponents p(x) satisfy the log-Hölder continuity, while the nonlinearity and underlying domain (A, Ω) is

In this work we solve a degenerate parabolic equation for the half line with Dirichlet boundary data, and use some results from the theory of Reproducing Kernel Hilbert Spaces to show that the null reachable space of this degenerate parabolic equation is a RKHS of analytic functions on a sector, whose reproducing kernel can be written in terms of the weighted Bergman kernel on the half plane C+.

No abstract is available for this article.

We consider the initial value problem (IVP) for the fractional Korteweg-de Vries equation (fKdV)(0.1){∂tu−Dxα∂xu+u∂xu=0,x,t∈R,0<α<1,u(x,0)=u0(x). It has been shown that the solutions to certain dispersive equations satisfy the propagation of regularity phenomena. More precisely, it deals in determine whether regularity of the initial data on the right hand side of the real line is propagated to the

The global boundedness and the hair trigger effect of solutions for the nonlinear nonlocal reaction-diffusion equation∂u∂t=Δu+μuα(1−κJ⁎uβ),inRN×(0,∞),N≥1 with α≥1, β,μ,κ>0 and u(x,0)=u0(x) are investigated. Under appropriate assumptions on J, it is proved that for any nonnegative and bounded initial condition, if α∈[1,α⁎) with α⁎=1+β for N=1,2 and α⁎=1+2βN for N>2, then the problem has a global bounded

In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some particular situations, this provides a strategy that could be used to compute approximations to the solution of the inverse problem. In the proofs, we use techniques

This paper is concerned with the following planar Schrödinger-Poisson system{−Δu+V(x)u+ϕu=f(x,u),x∈R2,Δϕ=u2,x∈R2, where V∈C(R2,[0,∞)) is axially symmetric and f∈C(R2×R,R) is of subcritical or critical exponential growth in the sense of Trudinger-Moser. We obtain the existence of a nontrivial solution or a ground state solution of Nehari-type and infinitely many solutions to the above system under weak

Boundary layer behaviour of a family of second order nonlinear differential equations with Neumann boundary condition arising from an order-reduction of a pseudo-differential equation in fluid dynamics is analysed. The problem is considered with two perturbation parameters μ,δ. Using asymptotic and numerical methods it is shown that by perturbing δ the problem in the limit μ→0 changes from a homogeneous

In this work we prove the existence of standing-wave solutions to the scalar non-linear Klein-Gordon equation in dimension one and the stability of the ground-state, the set which contains all the minima of the energy constrained to the manifold of the states sharing a fixed charge. For non-linearities which are combinations of two competing powers we prove that standing-waves in the ground-state are

In this paper, we study the cyclicity of periodic annulus and Hopf cyclicity in perturbing a quintic Hamiltonian system. The undamped system is hyper-elliptic, non-symmetric with a degenerate heteroclinic loop, which connects a hyperbolic saddle to a nilpotent saddle. We rigorously prove that the cyclicity is 3 for periodic annulus when the weak damping term has the same degree as that of the associated

This paper is concerned with the global well-posedness issue of the compressible viscoelastic fluids in the whole space RN,N≥2. The proof relies on the dispersive estimates to the linearized hyperbolic system combined with energy estimates to the hyperbolic-parabolic system. By exploiting the intrinsic structure of the system under some physical restrictions, we find that the compressible viscoelastic

For the Cauchy problem of multidimensional quasilinear hyperbolic systems of diagonal form without self-interaction, we show the global existence of classical solutions with small initial data. We also prove that the global solution will converge to a solution of the linearized system as time tends to infinity, and the convergence rate is also determined.

Models issued from ecology, chemical reactions and several other application fields lead to semi-linear parabolic equations with super-linear growth. Even if, in general, blow-up can occur, these models share the property that mass control is essential. In many circumstances, it is known that this L1 control is enough to prove the global existence of weak solutions. The theory is based on basic estimates

In this paper, we consider three-dimensional equatorial flows with constant vorticity beneath a wave train and above a flat bed in the β-plane approximation with centripetal forces. As a striking upshot, we show that the equatorial flow is necessarily irrotational and the free surface is necessarily flat if it exhibits a constant vorticity, owing to the presence of centripetal forces. For the case

We consider transmission problems for a coupling of a string and a beam with at least one of them being thermoelastic. The heat conduction is modeled by Fourier's law. We prove that the associated semigroup is exponentially stable when the string is thermoelastic. If only the beam is thermoelastic the system is always polynomially stable, but non exponentially stable for a large class of beams.

In this paper, we derive sharp bounds on the semigroup of the linearized incompressible Navier-Stokes equations near a stationary shear layer in the half space (R+2 or R+3), with Dirichlet boundary conditions, assuming that this shear layer in spectrally unstable for Euler equations. In the inviscid limit, due to the prescribed no-slip boundary conditions, vorticity becomes unbounded near the boundary

Let G be an infinite discrete countable amenable group acting continuously on a compact metrizable space X and Ω be a sequence in G. By using open covers of X, a topological invariant, the topological sequence entropy, is defined. It is shown that the topological sequence entropy can also be defined through relative spanning set or relative separate set. We prove that the topological sequence entropy

We first present a warped product manifold with boundary to show the non-uniqueness of the positive constant scalar curvature and positive constant boundary mean curvature equation. Next, we construct a smooth counterexample to show that the compactness of the set of “lower energy” solutions to the above equation fails when the dimension of the manifold is not less than 62.

The Landau–Lifshitz–Bloch equation perturbed by a space-dependent noise was proposed in [10] as a model for evolution of spins in ferromagnetic materials at the full range of temperatures, including the temperatures higher than the Curie temperature. In the case of a ferromagnet filling a bounded domain D⊂Rd, d=1,2,3, we show the existence of strong (in the sense of PDEs) martingale solutions. Furthermore

We consider travelling times of billiard trajectories in the exterior of an obstacle K on a two-dimensional Riemannian manifold M. We prove that given two obstacles with almost the same travelling times, the generalised geodesic flows on the non-trapping parts of their respective phase-spaces will have a time-preserving conjugacy. Moreover, if M has non-positive sectional curvature, we prove that if

For an optimal control problem governed by a controlled nonconvex sweeping process, we provide, using an exponential penalization technique, existence of solution and nonsmooth necessary conditions in the form of the Pontryagin maximum principle. Our results generalize known theorems in the literature, including those in [3] and [23], in several directions. Indeed, the main feature in our sweeping

The article is intended to study the Hopf−Zero bifurcation of a novel age-dependent predator−prey system with Monod−Haldane functional response comprising strong Allee effect. Here in this system the predators fertility function f(x) is regarded as a piecewise function with respect to their maturation period τ. The system is interpreted as a non-densely defined abstract Cauchy problem, and the condition

We introduce two shearlet-based Ginzburg–Landau energies, based on the continuous and the discrete shearlet transform. The energies result from replacing the elastic energy term of a classical Ginzburg–Landau energy by the weighted L2-norm of a shearlet transform. The asymptotic behaviour of sequences of these energies is analysed within the framework of Γ-convergence and the limit energy is identified

We propose a new solution to the blind source separation problem that factors mixed time-series signals into a sum of spatiotemporal modes, with the constraint that the temporal components are intrinsic mode functions (IMF's). The key motivation is that IMF's allow the computation of meaningful Hilbert transforms of non-stationary data, from which instantaneous time-frequency representations may be

We present a new infinite family of full spark equal norm tight frames in finite dimensions arising from a unitary group representation, where the underlying group is the semi-direct product of a cyclic group by a group of automorphisms. The only previously known algebraically constructed infinite families were the harmonic, Gabor and Dihedral frames. Our construction hinges on a theorem that requires

The Ando–Choi–Effros lifting theorem provides conditions under which a bounded linear mapping taking values in a quotient space can be lifted through the quotient map. We prove two versions of said theorem for regular maps between Banach lattices. Our conditions mirror the classical ones, but additionally taking into account the order structure.

Hydraulic fracturing (HF) treatment often involves particle migration and is applied for propping or plugging fractures. Particle migration behaviors, e.g., bridging, packing, and plugging, significantly affect the HF process. Hence, it is crucial to effectively simulate particle migration. In this study, a new numerical approach is developed based on a coupled element partition method (EPM). The EPM

Undrained deformation of dilative sand generates negative excess pore pressure. It enhances the strength, which is called dilative hardening. This increased suction is not permanent. The heterogeneity at the grain scale triggers localisations causing local volume changes. The negative hydraulic gradient drives fluid into dilating shear zones. It loosens the soil and diminishes the shear strength. It

X‐ray computed tomography (CT) imaging and digital image correlation techniques are applied to study spatial cracking behaviors of sandstone under uniaxial compression, in which the angle between precracks is 45°, 90°, and 135° and the crack depth is 7.5 mm and 10 mm, respectively. Layered anisotropy damages and spatial cracking evolution are quantitatively analyzed by the defined digital layered anisotropy

SIAM Journal on Numerical Analysis, Volume 58, Issue 4, Page 2019-2058, January 2020. In this paper, we propose a new stabilized projection-based proper orthogonal decomposition reduced order model (POD-ROM) for the numerical simulation of incompressible flows. The new method draws inspiration from successful numerical stabilization techniques used in the context of finite element (FE) methods, such

SIAM Journal on Matrix Analysis and Applications, Volume 41, Issue 3, Page 957-983, January 2020. In this paper, we propose a novel eigenvalue-based approach to solving the unbalanced orthogonal Procrustes problem. By making effective use of the necessary condition for the global minimizer and the orthogonal constraint, we shall first show that the unbalanced Procrustes problem can be equivalently

This paper describes the structure of invariant skew fields for linear actions of finite solvable groups on free skew fields in d generators. These invariant skew fields are always finitely generated, which contrasts with the free algebra case. For abelian groups or solvable groups G with a well-behaved representation theory it is shown that the invariant skew fields are free on |G|(d−1)+1 generators

A local expansion is proposed for two-point distributions involving an ultraviolet regularization in a four-dimensional globally hyperbolic space-time. The regularization is described by an infinite number of functions which can be computed iteratively by solving transport equations along null geodesics. We show that the Cauchy evolution preserves the regularized Hadamard structure. The resulting regularized

The present paper deals with some structural properties of transportation cost spaces, also known as Arens-Eells spaces, Lipschitz-free spaces and Wasserstein spaces. The main results of this work are: (1) A necessary and sufficient condition on an infinite metric space M, under which the transportation cost space on M contains an isometric copy of ℓ1. The obtained condition is applied to answer the

In this paper, we consider the Liouville-type problem of the three dimensional stationary incompressible Navier-Stokes equations, and establish an improved Liouville-type result only under the condition that the Lp norm of a velocity u is finite. Moreover, these results are extended to the MHD and Hall-MHD equations.

We discuss a model of a two-person, non-cooperative stochastic game, inspired by the discrete version of the red-and-black gambling problem presented by Dubins and Savage. Assume that two players hold certain amounts of money. At each stage of the game they simultaneously bid some part of their current fortune and the probability of winning or loosing depends on their bids. In many models of the red-and-black

The extended finite element method (XFEM) and the level set method (LSM) are applied to simulate the solidification phenomenon and the behavior of the liquid-solid phase transition. The temperature-based energy equation is loosely-coupled with the incompressible Navier-Stokes (INS) equations and solved by XFEM using the Stefan condition to express the energy conservation law for phase change. The INS

AbstractWe analyse the convergence of finite element discretizations of time-harmonic wave propagation problems. We propose a general methodology to derive stability conditions and error estimates that are explicit with respect to the wavenumber $k$. This methodology is formally based on an expansion of the solution in powers of $k$, which permits to split the solution into a regular, but oscillating