On a boundary value problem for an equation of the type of non-stationary filtration
On a class of nonlinear degenerate parabolic equations
On a nonlinear compactness lemma in .
On a nonlinear degenerate evolution equation with strong damping.
On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient.
On an over-determined problem of free boundary of a degenerate parabolic equation
This work is concerned with the inverse problem of determining initial value of the Cauchy problem for a nonlinear diffusion process with an additional condition on free boundary. Considering the flow of water through a homogeneous isotropic rigid porous medium, we have such desire: for every given positive constants and , to decide the initial value such that the solution satisfies , where . In this paper, we first establish a priori estimate and a more precise Poincaré type inequality...
On existence of the weak solution for nonlinear diffusion equation
The paper concerns the existence of bounded weak solutions of a anonlinear diffusion equation with nonhomogeneous mixed boundary conditions.
On forced periodic solutions of superlinear quasi-parabolic problems.
On fully practical finite element approximations of degenerate Cahn-Hilliard systems
We consider a model for phase separation of a multi-component alloy with non-smooth free energy and a degenerate mobility matrix. In addition to showing well-posedness and stability bounds for our approximation, we prove convergence in one space dimension. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. We discuss also how our approximation has to be modified in order to be applicable to a logarithmic free energy. Finally numerical experiments with...
On fully practical finite element approximations of degenerate Cahn-Hilliard systems
We consider a model for phase separation of a multi-component alloy with non-smooth free energy and a degenerate mobility matrix. In addition to showing well-posedness and stability bounds for our approximation, we prove convergence in one space dimension. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. We discuss also how our approximation has to be modified in order to be applicable to a logarithmic free energy. Finally numerical experiments...
On gradient estimates and other qualitative properties of solutions of nonlinear non autonomous parabolic systems.
On higher-order semilinear parabolic equations with measures as initial data
We consider th-order semilinear parabolic equations in , with Dirac’s mass as the initial function. We show that for , the Cauchy problem admits...
On maximum principle for weak subsolutions of degenerate parabolic linear equations
Sufficient conditions are obtained so that a weak subsolution of , bounded from above on the parabolic boundary of the cylinder , turns out to be bounded from above in .
On solutions of a perturbed fast diffusion equation
The paper concerns the (local and global) existence, nonexistence, uniqueness and some properties of nonnegative solutions of a nonlinear density dependent diffusion equation with homogeneous Dirichlet boundary conditions.
On some improperly posed problem for a degenerate nonlinear parabolic equation.
On some properties of solutions of quasilinear degenerate parabolic equations in
We study the asymptotic behaviour near infinity of the weak solutions of the Cauchy-problem.
On the Cauchy problem and initial traces for a class of evolution equations with strongly nonlinear sources
On the Cauchy problem for a degenerate parabolic differential equation.
On the Cauchy problem for the equation of one-dimensional non-stationary filtration with non-continuous initial data
On the Cauchy problem of a quasilinear degenerate parabolic equation.