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 inertial manifolds for reaction-diffusion equations on genuinely high-dimensional thin domains
We study a family of semilinear reaction-diffusion equations on spatial domains , ε > 0, in lying close to a k-dimensional submanifold ℳ of . As ε → 0⁺, the domains collapse onto (a subset of) ℳ. As proved in [15], the above family has a limit equation, which is an abstract semilinear parabolic equation defined on a certain limit phase space denoted by . The definition of , given in the above paper, is very abstract. One of the objectives of this paper is to give more manageable characterizations...
On initial boundary value problems with equivalued surface for nonlinear parabolic equations.
On internal approximations of parabolic problems
On iterative solution of nonlinear heat-conduction and diffusion problems
The present paper deals with the numerical solution of the nonlinear heat equation. An iterative method is suggested in which the iterations are obtained by solving linear heat equation. The convergence of the method is proved under very natural conditions on given input data of the original problem. Further, questions of convergence of the Galerkin method applied to the original equation as well as to the linear equations in the above mentioned iterative method are studied.
On -convergence of Rothe’s method
On -estimates for solutions of the Cauchy problem for parabolic differential equations
On L2 Decay of Weak Solutions of the Navier-Stokes Equations in Rn.
On linearizing systems of diffusion equations.
On long time behaviour of a class of reaction-diffusion models
On Maximal Functions and Parabolic Limits.
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 mixed problems for quasilinear second-order systems.
On multigrid for linear complementarity problems with application to American-style options.
On multiresolution methods in numerical analysis.
On nonlinear, nonconvex evolution inclusions
We consider a nonlinear evolution inclusion driven by an m-accretive operator which generates an equicontinuous nonlinear semigroup of contractions. We establish the existence of extremal integral solutions and we show that they form a dense, -subset of the solution set of the original Cauchy problem. As an application, we obtain “bang-bang”’ type theorems for two nonlinear parabolic distributed parameter control systems.
On nonlocal problems for ordinary differential equations and on a nonlocal parabolic transmission problem.
On nonstandard potentials in a Stefan problem.
On Numerical Asymptotic Behavior of Finite Element Solutions for Parabolic Equations.
On numerical solutions of partial differential equations by the decomposition method