The Dirichlet boundary conditions and related natural boundary conditions in strengthened Sobolev spaces for discretized parabolic problems.
The Dirichlet problem for a class of nonlinear degenerate parabolic equations.
The Dirichlet problem for a parabolic semilinear differential equation in an unbounded domain.
The existence and behavior of solutions for nonlocal boundary problems.
The finite element solution of parabolic equations
In contradistinction to former results, the error bounds introduced in this paper are given for fully discretized approximate soltuions of parabolic equations and for arbitrary curved domains. Simplicial isoparametric elements in -dimensional space are applied. Degrees of accuracy of quadrature formulas are determined so that numerical integration does not worsen the optimal order of convergence in -norm of the method.
The first initial-boundary value problem for quasilinear second order parabolic equations
The fundamental solution of a modified Oseen problem.
The generalized Burgers equation with and without a time delay.
The monotone method on the sub-strongly coupled reaction-diffusion systems
The principal spectrum for linear nonautonomous parabolic PDEs of second order: Space-independent case
We show that the study of the principal spectrum of a linear nonautonomous parabolic PDE of second order on a bounded domain, with the Dirichlet or Neumann boundary conditions, reduces to the investigation of the spectrum of the linear nonautonomous ODE v̇ = a(t)v.
The solutions of the quasilinear Keller-Segel system with the volume filling effect do not blow up whenever the Lyapunov functional is bounded from below
In [2] we proved two kinds of mechanisms of preventing the blow up in a quasilinear non-uniformly parabolic Keller-Segel systems. One of them was a priori boundedness from below of the Lyapunov functional. In fact, we were able to present a condition under which the Lyapunov functional is bounded from below and a solution exists globally. In the present paper we prove that whenever the Lyapunov functional is bounded from below the solution exists globally.
The support shrinking properties for solutions of quasilinear parabolic equations with strong absorption terms
Thermistor problem: a nonlocal parabolic problem.
Topological properties of nonlinear evolution equations
Transition from decay to blow-up in a parabolic system.
Transition from decay to blow-up in a parabolic system
We show a locally uniform bound for global nonnegative solutions of the system , in , on , where , and is a bounded domain in , . In particular, the trajectories starting on the boundary of the domain of attraction of the zero solution are global and bounded.
�?tude de l'unicité des solutions antipériodiques pour des équations d'évolution non linéaires
Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions.
Über die Existenz von unendlich vielen periodischen Lösungen einer einfachen Temperaturregelung.
Un théorème de valeurs intermédiaires dans les espaces de Sobolev et applications