Wave propagation in a lattice KPP equation in random media.
Waves of Autocrine Signaling in Patterned Epithelia
A biophysical model describing long-range cell-to-cell communication by a diffusible signal mediated by autocrine loops in developing epithelia in the presence of a morphogenetic pre-pattern is introduced. Under a number of approximations, the model reduces to a particular kind of bistable reaction-diffusion equation with strong heterogeneity. In the case of the heterogeneity in the form of a long strip a detailed analysis of signal propagation is...
Weak- solutions for a model of self-gravitating particles with an external potential
The existence of solutions to a nonlinear parabolic equation describing the temporal evolution of a cloud of self-gravitating particles with a given external potential is studied in weak- spaces (i.e. Markiewicz spaces). The main goal is to prove the existence of global solutions and to study their large time behaviour.
Weak periodic solutions of the boundary value problem for nonlinear heat equation
The paper deals with the existence of periodic solutions of the boundary value problem for nonlinear heat equation, where various types of nonlinearities are considered. The proofs are based on the investigation of Liapunov-Schmidt bifurcation system via Leray-Schauder degree theory.
Weak Solutions for a Fourth Order Degenerate Parabolic Equation
We consider an initial-boundary value problem for a fourth order degenerate parabolic equation. Under some assumptions on the initial value, we establish the existence of weak solutions by the discrete-time method. The asymptotic behavior and the finite speed of propagation of perturbations of solutions are also discussed.
Weak solutions for a viscous -Laplacian equation.
Weak Solutions for Nonlinear Parabolic Equations with Variable Exponents
In this work, we study the existence and uniqueness of weak solutions of fourth-order degenerate parabolic equation with variable exponent using the difference and variation methods.
Weak solutions for quasilinear degenerate parabolic systems.
Weak solutions to a time-dependent heat equation with nonlocal radiation boundary condition and arbitrary -summable right-hand side
We consider a model for transient conductive-radiative heat transfer in grey materials. Since the domain contains an enclosed cavity, nonlocal radiation boundary conditions for the conductive heat-flux are taken into account. We generalize known existence and uniqueness results to the practically relevant case of lower integrable heat-sources, and of nonsmooth interfaces. We obtain energy estimates that involve only the norm of the heat sources for exponents close to one. Such estimates are...
Weighted energy-dissipation functionals for gradient flows
We investigate a global-in-time variational approach to abstract evolution by means of the weighted energy-dissipation functionals proposed by Mielke and Ortiz [ESAIM: COCV14 (2008) 494–516]. In particular, we focus on gradient flows in Hilbert spaces. The main result is the convergence of minimizers and approximate minimizers of these functionals to the unique solution of the gradient flow. Sharp convergence rates are provided and the convergence analysis is combined with time-discretization....
Weighted energy-dissipation functionals for gradient flows
We investigate a global-in-time variational approach to abstract evolution by means of the weighted energy-dissipation functionals proposed by Mielke and Ortiz [ESAIM: COCV14 (2008) 494–516]. In particular, we focus on gradient flows in Hilbert spaces. The main result is the convergence of minimizers and approximate minimizers of these functionals to the unique solution of the gradient flow. Sharp convergence rates are provided and the convergence analysis is combined with time-discretization....
Well-Posedness of a Semilinear Heat Equation with Weak Initial Data.
Well-posedness of a thermo-mechanical model for shape memory alloys under tension
We present a model of the full thermo-mechanical evolution of a shape memory body undergoing a uniaxial tensile stress. The well-posedness of the related quasi-static thermo-inelastic problem is addressed by means of hysteresis operators techniques. As a by-product, details on a time-discretization of the problem are provided.