A blow-up mechanism for a chemotaxis model
A boundary control problem with a nonlinear reaction term.
A class of nonlocal parabolic problems occurring in statistical mechanics
We consider parabolic equations with nonlocal coefficients obtained from the Vlasov-Fokker-Planck equations with potentials. This class of equations includes the classical Debye system from electrochemistry as well as an evolution model of self-attracting clusters under friction and fluctuations. The local in time existence of solutions to these equations (with no-flux boundary conditions) and properties of stationary solutions are studied.
A class of time discrete schemes for a phase–field system of Penrose–Fife type
In this paper, a phase field system of Penrose–Fife type with non–conserved order parameter is considered. A class of time–discrete schemes for an initial–boundary value problem for this phase–field system is presented. In three space dimensions, convergence is proved and an error estimate linear with respect to the time–step size is derived.
A corrector result for -converging parabolic problems with time-dependent coefficients
A counterexample in regularity theory for parabolic systems
A criterion of Petrowsky's kind for a degenerate quasilinear parabolic equation.
The celebrated criterion of Petrowsky for the regularity of the latest boundary point, originally formulated for the heat equation, is extended to the so-called p-parabolic equation. A barrier is constructed by the aid of the Barenblatt solution.
A decomposition method for a semilinear boundary value problem with a quadratic nonlinearity.
A degenerate parabolic equation in noncylindrical domains.
A few results on a class of degenerate parabolic equations
A Gamma-convergence argument for the blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions
A generalized maximum principle and estimates of max vrai for nonlinear parabolic boundary value problems
A Hopf bifurcation generated by variation of the domain
A maximal regularity result with applications to parabolic problems with nonhomogeneous boundary conditions
A mixed semilinear parabolic problem from combustion theory.
A model of a radially symmetric cloud of self-attracting particles
We consider a parabolic equation which describes the gravitational interaction of particles. Existence of solutions and their convergence to stationary states are studied.
A multiplicity result for a class of quasilinear elliptic and parabolic problems.
A Neumann problem for a convection-diffusion equation on the half-line
We study solutions to a nonlinear parabolic convection-diffusion equation on the half-line with the Neumann condition at x=0. The analysis is based on the properties of self-similar solutions to that problem.
A nonlinear diffusion equation with nonlinear boundary conditions: Method of lines
A nonlinear heat equation with temperature-dependent parameters.