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  • A convex approach to the Gilbert–Steiner problem
    Interfaces Free Bound. (IF 0.718) Pub Date : 2020-07-06
    Mauro Bonafini; Édouard Oudet

    We describe a convex relaxation for the Gilbert–Steiner problem both in Rd and on manifolds, extending the framework proposed in [10], and we discuss its sharpness by means of calibration type arguments. The minimization of the resulting problem is then tackled numerically and we present results for an extensive set of examples. In particular we are able to address the Steiner tree problem on surfaces

    更新日期:2020-07-20
  • Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics
    Interfaces Free Bound. (IF 0.718) Pub Date : 2020-07-06
    Georgy Kitavtsev; Roman M. Taranets

    In this paper, we extend the results of [8] by proving exponential asymptotic $H^1$-convergence of solutions to a one-dimensional singular heat equation with $L^2$-source term that describe evolution of viscous thin liquid sheets while considered in the Lagrange coordinates. Furthermore, we extend this asymptotic convergence result to the case of a time inhomogeneous source. This study has also independent

    更新日期:2020-07-20
  • Segregation effects and gap formation in cross-diffusion models
    Interfaces Free Bound. (IF 0.718) Pub Date : 2020-07-06
    Martin Burger; José A. Carrillo; Jan-Frederik Pietschmann; Markus Schmidtchen

    In this paper, we extend the results of [8] by proving exponential asymptotic $H^1$-convergence of solutions to a one-dimensional singular heat equation with $L^2$-source term that describe evolution of viscous thin liquid sheets while considered in the Lagrange coordinates. Furthermore, we extend this asymptotic convergence result to the case of a time inhomogeneous source. This study has also independent

    更新日期:2020-07-20
  • From individual-based mechanical models of multicellular systems to free-boundary problems
    Interfaces Free Bound. (IF 0.718) Pub Date : 2020-07-06
    Tommaso Lorenzi; Philip J. Murray; Mariya Ptashnyk

    In this paper we present an individual-based mechanical model that describes the dynamics of two contiguous cell populations with different proliferative and mechanical characteristics. An off-lattice modelling approach is considered whereby: (i) every cell is identified by the position of its centre; (ii) mechanical interactions between cells are described via generic nonlinear force laws; and (iii)

    更新日期:2020-07-20
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