A nonlinear heat equation with temperature-dependent parameters.
A nonlinear oblique derivative boundary value problem for the heat equation : analogy with the porous medium equation
A note on estimates for quasilinear parabolic equations.
A Numerical Approach of the sentinel method for distributed parameter systems
In this paper we consider the problem of detecting pollution in some non linear parabolic systems using the sentinel method. For this purpose we develop and analyze a new approach to the discretization which pays careful attention to the stability of the solution. To illustrate convergence properties we give some numerical results that present good properties and show new ways for building discrete sentinels.
A parabolic - elliptic variational inequality.
A parabolic quasilinear problem for linear growth functionals.
We prove existence and uniqueness of solutions for the Dirichlet problem for quasilinear parabolic equations in divergent form for which the energy functional has linear growth.
A parabolic quasi-variational inequality arising in a superconductivity model
A parabolic system in a weighted Sobolev space
We examine the regularity of solutions of a certain parabolic system in the weighted Sobolev space , where the weight is of the form , r is the distance from a distinguished axis and μ ∈ (0,1).
A phase-field model of grain boundary motion
We consider a phase-field model of grain structure evolution, which appears in materials sciences. In this paper we study the grain boundary motion model of Kobayashi-Warren-Carter type, which contains a singular diffusivity. The main objective of this paper is to show the existence of solutions in a generalized sense. Moreover, we show the uniqueness of solutions for the model in one-dimensional space.
A posteriori error control for the Allen–Cahn problem : circumventing Gronwall’s inequality
Phase-field models, the simplest of which is Allen–Cahn’s problem, are characterized by a small parameter that dictates the interface thickness. These models naturally call for mesh adaptation techniques, which rely on a posteriori error control. However, their error analysis usually deals with the underlying non-monotone nonlinearity via a Gronwall argument which leads to an exponential dependence on . Using an energy argument combined with a topological continuation argument and a spectral...
A posteriori error control for the Allen–Cahn problem: circumventing Gronwall's inequality
Phase-field models, the simplest of which is Allen–Cahn's problem, are characterized by a small parameter ε that dictates the interface thickness. These models naturally call for mesh adaptation techniques, which rely on a posteriori error control. However, their error analysis usually deals with the underlying non-monotone nonlinearity via a Gronwall argument which leads to an exponential dependence on ε-2. Using an energy argument combined with a topological continuation argument and...
A posteriori estimates for the Cahn–Hilliard equation with obstacle free energy
We derive a posteriori estimates for a discretization in space of the standard Cahn–Hilliard equation with a double obstacle free energy. The derived estimates are robust and efficient, and in practice are combined with a heuristic time step adaptation. We present numerical experiments in two and three space dimensions and compare our method with an existing heuristic spatial mesh adaptation algorithm.
A priori bounds for solutions of parabolic problems and applications
A probabilistic approach to the trace at the boundary for solutions of a semilinear parabolic partial differential equation.
A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees
A qualitative study on a parabolic free boundary problem.
A quasi-linear parabolic system of chemotaxis.
A regularity theorem for curvature flows.
A remark on the large time behavior of solutions of viscous Hamilton-Jacobi equations
A remark on the note : “Partial Hölder continuity of the spatial derivatives of the solutions to nonlinear parabolic systems with quadratic growth”