EuDML | Browse

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 $K$ and $T_{0}$ , to decide the initial value $u_{0}$ such that the solution $u (x, t)$ satisfies ${sup}_{x \in H_{u} (T_{0})} | x | \geq K$ , where $H_{u} (T_{0}) = {x \in ℝ^{N} : u (x, T_{0}) > 0}$ . In this paper, we first establish a priori estimate $u_{t} \geq C (t) u$ and a more precise Poincaré type inequality...

On existence of the weak solution for nonlinear diffusion equation

Juraj Zeman (1991)

Applications of Mathematics

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.

Boldrini, José Luiz, Crema, Janete (1998)

Electronic Journal of Differential Equations (EJDE) [electronic only]

On fully practical finite element approximations of degenerate Cahn-Hilliard systems

John W. Barrett, James F. Blowey, Harald Garcke (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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

John W. Barrett, James F. Blowey, Harald Garcke (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

On gradient estimates and other qualitative properties of solutions of nonlinear non autonomous parabolic systems.

S.N. Antonsev, J.I. Díaz (2009)

RACSAM

On higher-order semilinear parabolic equations with measures as initial data

Victor Galaktionov (2004)

Journal of the European Mathematical Society

We consider $2 m$ th-order $(m \geq 2)$ semilinear parabolic equations $u_{t} = - {(- Δ)}^{m} u \pm {| u |}^{p - 1} u$ in $ℛ^{N} \times ℝ_{+}$ $(p > 1)$ , with Dirac’s mass $δ (x)$ as the initial function. We show that for $p < p_{0} = 1 + 2 m / N$ , the Cauchy problem admits...

On maximum principle for weak subsolutions of degenerate parabolic linear equations

Salvatore Bonafede (1994)

Commentationes Mathematicae Universitatis Carolinae

Sufficient conditions are obtained so that a weak subsolution of $(0.1)$ , bounded from above on the parabolic boundary of the cylinder $Q$ , turns out to be bounded from above in $Q$ .

On solutions of a perturbed fast diffusion equation

Ján Filo (1987)

Aplikace matematiky

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.

Hayasida, K. (2000)

Zeitschrift für Analysis und ihre Anwendungen

On some properties of solutions of quasilinear degenerate parabolic equations in $ℝ^{m} \times (0, + \infty)$

Salvatore Bonafede, Francesco Nicolosi (2004)

Mathematica Bohemica

We study the asymptotic behaviour near infinity of the weak solutions of the Cauchy-problem.

Currently displaying 1 – 20 of 37

Page 1 Next

Displaying 1 – 20 of 37

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 $L^{p} (0, T; B)$ .

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

On existence of the weak solution for nonlinear diffusion equation

On forced periodic solutions of superlinear quasi-parabolic problems.

On fully practical finite element approximations of degenerate Cahn-Hilliard systems

On fully practical finite element approximations of degenerate Cahn-Hilliard systems

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

On maximum principle for weak subsolutions of degenerate parabolic linear equations

On solutions of a perturbed fast diffusion equation

On some improperly posed problem for a degenerate nonlinear parabolic equation.

On some properties of solutions of quasilinear degenerate parabolic equations in $ℝ^{m} \times (0, + \infty)$

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.

Currently displaying 1 – 20 of 37