On an approximate solution for quasilinear parabolic equations
On an optimal control problem for a quasilinear parabolic equation
An optimal control problem governed by a quasilinear parabolic equation with additional constraints is investigated. The optimal control problem is converted to an optimization problem which is solved using a penalty function technique. The existence and uniqueness theorems are investigated. The derivation of formulae for the gradient of the modified function is explainedby solving the adjoint problem.
On basin of zero-solutions to a semilinear parabolic equation with Ornstein-Uhlenbeck operator.
On blow-up and asymptotic behavior of solutions for some semilinear parabolic systems of second order
In questo lavoro sotto queste ipotesi si ottengono alcune condizioni di non esistenza e di esistenza delle soluzioni per alcuni sistemi parabolici semilineari del secondo ordine. Inoltre si studia il comportamento asintotico di alcune soluzioni.
On blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions
We obtain some sufficient conditions under which solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions tend to zero or blow up in a finite time. We also give the asymptotic behavior of solutions which tend to zero as . Finally, we obtain the asymptotic behavior near the blow-up time of certain blow-up solutions and describe their blow-up set.
On blow-up at space infinity for semilinear heat equations
On blowup of a solution to a Sobolev-type equation with a nonlocal source.
On Chemotaxis Models with Cell Population Interactions
This paper extends the volume filling chemotaxis model [18, 26] by taking into account the cell population interactions. The extended chemotaxis models have nonlinear diffusion and chemotactic sensitivity depending on cell population density, which is a modification of the classical Keller-Segel model in which the diffusion and chemotactic sensitivity are constants (linear). The existence and boundedness of global solutions of these models are discussed and...
On difference schemes for quasilinear evolution problems.
On evolution equations for moving domains.
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 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 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 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 Parabolic Systems with Variational Structure.
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.