Parabolic boundary-value problems with equivalued surface on the domain with a thin layer.
Parabolic Differential Equations and Inequalities with Several Time Variables.
Parabolic equations with multiple singularities
Parabolic equations with robin type boundary conditions in a non-rectangular domain.
Parabolic equations with VMO coefficients in Morrey spaces.
Parabolic initial-boundary value problems in Orlicz spaces
We prove some time mollification properties and imbedding results in inhomogeneous Orlicz-Sobolev spaces which allow us to solve a second order parabolic equation in Orlicz spaces.
Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces
We obtain the global weighted Morrey-type regularity of the solution of the regular oblique derivative problem for linear uniformly parabolic operators with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized weighted Morrey space Mp,ϕ(Q, w), than the strong solution belongs to the generalized weighted Sobolev- Morrey space [...] W˙2,1p,φ(Q,ω).
Parabolic-elliptic correspondence of a three-level finite difference approximation to the heat equation.
Partial Hölder continuity of the spatial derivatives of the solutions to nonlinear parabolic systems with quadratic growth
Periodic problems and problems with discontinuities for nonlinear parabolic equations
In this paper we study nonlinear parabolic equations using the method of upper and lower solutions. Using truncation and penalization techniques and results from the theory of operators of monotone type, we prove the existence of a periodic solution between an upper and a lower solution. Then with some monotonicity conditions we prove the existence of extremal solutions in the order interval defined by an upper and a lower solution. Finally we consider problems with discontinuities and we show that...
Periodic solutions of evolution -Laplacian equations with a nonlinear convection term.
Periodic solutions of nonlinear boundary value problems of the second kind
Periodic systems dependent on parameters.
Perona-Malik equation: properties of explicit finite volume scheme
The Perona–Malik nonlinear parabolic problem, which is widely used in image processing, is investigated in this paper from the numerical point of view. An explicit finite volume numerical scheme for this problem is presented and consistency property is proved.
Principio Inverso Del Maximo Para Ecuaciones Parabolicas Periodicas.
Problème d'évolution parabolique pour une classe d'opérateurs elliptiques dégénérés
Problème d'évolution parabolique pour une classe d'opérateurs elliptiques et dégénérés
Proper orthogonal decomposition for optimality systems
Proper orthogonal decomposition (POD) is a powerful technique for model reduction of non-linear systems. It is based on a Galerkin type discretization with basis elements created from the dynamical system itself. In the context of optimal control this approach may suffer from the fact that the basis elements are computed from a reference trajectory containing features which are quite different from those of the optimally controlled trajectory. A method is proposed which avoids this problem of unmodelled...
Properties of positive solution for nonlocal reaction-diffusion equation with nonlocal boundary.
Pullback attractors for nonautonomous parabolic equations involving weighted p-Laplacian operators
Using the asymptotic a priori estimate method, we prove the existence of pullback attractors for nonautonomous quasilinear degenerate parabolic equations involving weighted p-Laplacian operators in bounded domains, without restriction on the growth order of the polynomial type nonlinearity and on the exponential growth of the external force. The results obtained improve some recent ones for nonautonomous reaction-diffusion equations. Moreover, a relationship between pullback attractors and uniform...