A nonlinear oblique derivative boundary value problem for the heat equation. Part 1 : basic results
A nonlinear oblique derivative boundary value problem for the heat equation. Part 2 : singular self-similar solutions
A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology.
We present some results on the mathematical treatment of a global two-dimensional diffusive climate model. The model is based on a long time averaged energy balance and leads to a nonlinear parabolic equation for the averaged surface temperature. The spatial domain is a compact two-dimensional Riemannian manifold without boundary simulating the Earth. We prove the existence of bounded weak solutions via a fixed point argument. Although, the uniqueness of solutions may fail, in general, we give a...
A note on the existence of solution for semilinear heat equations with polynomial growth nonlinearity
The existence of weak solution for periodic-Dirichlet problem to semilinear heat equations with superlinear growth non-linear term is treated.
A notion of renormahzed solution of the study of a general conservation law.
A priori bounds for global solutions of a semilinear parabolic problem.
A priori bounds for solutions of parabolic problems and applications
A priori bounds for solutions of parabolic problems and applications
We review some recent results concerning a priori bounds for solutions of superlinear parabolic problems and their applications.
A priori estimates for global solutions and multiple equilibria of a superlinear parabolic problem involving measures.
A priori estimates of solutions of superlinear problems
In this survey we consider superlinear parabolic problems which possess both blowing-up and global solutions and we study a priori estimates of global solutions.
A problem with nonlocal boundary conditions for a quasilinear parabolic equation.
A qualitative theory for parabolic problems under dynamical boundary conditions.
A remark on parabolic equations.
A semilinear parabolic boundary-value problem in bioreactors theory.
A singular radially symmetric problem in electrolytes theory
Existence of radially symmetric solutions (both stationary and time dependent) for a parabolic-elliptic system describing the evolution of the spatial density of ions in an electrolyte is studied.
A stability result for parameter identification problems in nonlinear parabolic problems.
A survey of results on nonlinear Venttsel problems
We review the recent results for boundary value problems with boundary conditions given by second-order integral-differential operators. Particular attention has been paid to nonlinear problems (without integral terms in the boundary conditions) for elliptic and parabolic equations. For these problems we formulate some statements concerning a priori estimates and the existence theorems in Sobolev and Hölder spaces.
A system of impulsive degenerate nonlinear parabolic functional- differential inequalities.
A temperature control problem.
Addendum to the paper “Finite element solution of quasistationary nonlinear magnetic field”