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...
Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term
Quelques résultats sur les solutions de systèmes d'inéquations de type parabolique
On considère un opérateur défini paroù est une application de dans ( ouvert quelconque de ),
Quenching time of solutions for some nonlinear parabolic equations with Dirichlet boundary condition and a potential.
Radiative Heating of a Glass Plate
This paper aims to prove existence and uniqueness of a solution to the coupling of a nonlinear heat equation with nonlinear boundary conditions with the exact radiative transfer equation, assuming the absorption coefficient to be piecewise constant and null for small values of the wavelength as in the paper of N. Siedow, T. Grosan, D. Lochegnies, E. Romero, “Application of a New Method for Radiative Heat Tranfer to Flat Glass Tempering”, J. Am. Ceram. Soc., 88(8):2181-2187 (2005). An important...
Reaction-diffusion in nonsmooth and closed domains.
Recovery of an unknown flux in parabolic problems with nonstandard boundary conditions: Error estimates
In this paper, we consider a 2nd order semilinear parabolic initial boundary value problem (IBVP) on a bounded domain , with nonstandard boundary conditions (BCs). More precisely, at some part of the boundary we impose a Neumann BC containing an unknown additive space-constant , accompanied with a nonlocal (integral) Dirichlet side condition. We design a numerical scheme for the approximation of a weak solution to the IBVP and derive error estimates for the approximation of the solution and...
Refinement of an Lp-Estimate of Solonnikov for a Parabolic Equation of the Second Order with Conormal Boundary Condition.
Regional boundary observability: a numerical approach
In this paper we review the concept of regional boundary observability, developed in (Michelitti, 1976), by means of sensor structures. This leads to the so-called boundary strategic sensors. A characterization of such sensors which guarantees regional boundary observability is given. The results obtained are applied to a two-dimensional system, and various cases of sensors are considered. We also describe an approach which leads to the estimation of the initial boundary state, which is illustrated...