Related papers: Parabolic equations in time dependent domains
We consider semilinear parabolic equations with nonlinear boundary conditions. We give conditions which guarantee global existence of solutions as well as blow-up in finite time of all solutions with nontrivial initial data. The results…
The aim of this work is studding the behavior of solutions of initial boundary problem for degenerated nonlinear parabolic equation of the second order, conditions of existence and non-existence in whole by time solutions, is establish.
Parasupersymmetry of the one dimensional time-dependent Schr\"odinger equation is established. It is intimately connected with a chain of the time-dependent Darboux transformations. As an example a parasupersymmetric model of…
In the present article we investigate a boundary problem with non-local conditions for mixed parabolic-hyperbolic type equation with three lines of type changing. Considered mixed domain contains a rectangle as a parabolic part and three…
We prove regularity estimates for time derivatives of a large class of nonlinear parabolic partial differential systems. This includes the instationary (symmetric) p-Laplace system and models for non Newtonien fluids of powerlaw or Carreau…
We prove the homogenization of fully nonlinear parabolic equations with periodic oscillating Dirichlet boundary conditions on certain general prescribed space-time domains. It was proved in [9,10] that for elliptic equations, the…
In this paper we study a class of nonlinearities for which a nonlocal parabolic equation with Neumann-Robin boundary conditions, for $p$-Laplacian, has finite time blow-up solutions.
In this work we consider the asymptotic behavior of the nonlinear semigroup defined by a semilinear parabolic problem with homogeneous Neumann boundary conditions posed in a bounded region of the plane that degenerates into a line segment…
We study a two-point free boundary problem in a sector for a quasilinear parabolic equation. The boundary conditions are assumed to be spatially and temporally "self-similar" in a special way. We prove the existence, uniqueness and…
We establish H\"older estimates for the time derivative of solutions of non-local parabolic equations under mild assumptions for the boundary data. As a consequence we are able to extend the Evans-Krylov estimate for rough kernels to…
In this article, we consider non-smooth time-dependent domains and single-valued, smoothly varying directions of reflection at the boundary. In this setting, we first prove existence and uniqueness of strong solutions to stochastic…
Time-periodic solutions to partial differential equations of parabolic type corresponding to an operator that is elliptic in the sense of Agmon-Douglis-Nirenberg are investigated. In the whole- and half-space case we construct an explicit…
This paper is concerned with the weak solvability of fully nonlinear parabolic variational inequalities with time dependent convex constraints. As possible approaches to such problems, there are for instance the time-discretization method…
Under a precise nonlinearity-diffusivity condition we establish the decay of space-periodic entropy solutions of a multidimensional degenerate nonlinear parabolic equation.
We consider both divergence and non-divergence parabolic equations on a half space in weighted Sobolev spaces. All the leading coefficients are assumed to be only measurable in the time and one spatial variable except one coefficient, which…
We prove the existence of strong and weak solutions to the semilinear wave equation with coefficients depending both on time and space variables, with continuous nonlinearity satisfying the sign condition. The uniqueness is proven under…
We establish $L_{q,p}$-estimates and solvability for mixed Dirichlet-conormal problems for parabolic equations in a cylindrical Reifenberg-flat domain with a rough time-dependent separation.
We show the continuous dependence of solutions of linear nonautonomous second order parabolic partial differential equations (PDEs) with bounded delay on coefficients and delay. The assumptions are very weak: only convergence in the weak-*…
We consider a priori estimates of possibly sign-changing solutions to superlinear parabolic problems and their applications (blow-up rates, energy blow-up, continuity of blow-up time, existence of nontrivial steady states etc). Our…
We establish uniqueness for sign-changing solutions to Trudinger's parabolic equation with time dependent $C^2$ Dirichlet boundary data.