Nonlinear boundary problems for a quasilinear parabolic equation

Nonlinear Transmission Problems for Quasilinear Parabolic Systems

We study degenerate quasilinear parabolic systems in two different domains, which are connected by a nonlinear transmission condition at their interface. For a large class of models, including those modeling pollution aggression on stones and chemotactic movements of bacteria, we prove global existence, uniqueness and stability of the solutions.

Blow-up Behavior for a Quasilinear Parabolic Equation with Nonlinear Boundary Condition

In this paper, we study the solution of an initial boundary value problem for a quasilinear parabolic equation with a nonlinear boundary condition. We first show that any positive solution blows up in finite time. For a monotone solution, we have either the single blow-up point on the boundary, or blow-up on the whole domain, depending on the parameter range. Then, in the single blow-up point c...

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

A numerical scheme for solving nonlinear backward parabolic problems

‎In this paper a nonlinear backward parabolic problem in one‎ ‎dimensional space is considered‎. ‎Using a suitable iterative‎ ‎algorithm‎, ‎the problem is converted to a linear backward parabolic‎ ‎problem‎. ‎For the corresponding problem‎, ‎the backward finite‎ ‎differences method with suitable grid size is applied‎. ‎It is shown‎ ‎that if the coefficients satisfy some special conditions‎, ‎th...

Stable and Unstable Manifolds for Quasilinear Parabolic Problems with Fully Nonlinear Dynamical Boundary Conditions

We develop a wellposedness and regularity theory for a large class of quasilinear parabolic problems with fully nonlinear dynamical boundary conditions. Moreover, we construct and investigate stable and unstable local invariant manifolds near a given equilibrium. In a companion paper we treat center, center–stable and center–unstable manifolds for such problems and investigate their stability p...