Identification of a Quasilinear Parabolic Equation from Final Data

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

Computing Optimal Control with a Quasilinear Parabolic Partial Differential Equation

This paper presents the numerical solution of a constrained optimal control problem (COCP) for quasilinear parabolic equations. The COCP is converted to unconstrained optimization problem (UOCP) by applying the exterior penalty function method. Necessary optimality conditions for the considered problem are established. The computing optimal controls are helped to identify the unknown coefficien...

Error Analysis of an Equation Error Method for the Identification of the Diffusion Coefficient in a Quasi-linear Parabolic Differential Equation

We consider the inverse problem of reconstructing the diiusion coeecient in a quasilinear parabolic diierential equation in divergence form from measurements of the solution at a nite number of points in the interior of the domain. An equation error method is developed which transforms the inverse problem into a system of linear operator equations for the diiusion coeecient, and which can be so...

Global Existence, Uniqueness, and Continuous Dependence for a Reaction-diffusion Equation with Memory

Global existence, uniqueness and continuous dependence on initial data are established for a quasilinear functional reaction-diiusion equation which arises from a two-dimensional energy balance climate model. Our approach relies heavily on the so-called stability estimates for linear evolution equations of parabolic type (cf. 6]).

Existence and Uniqueness of Solution for a Parabolic Quasilinear Problem for Linear Growth Functionals with L1 Data

We prove existence and uniqueness of solutions for the Dirichlet problem for quasilinear parabolic equations in divergent form for which the energy functional has linear growth. A tipical example of energy functional we consider is the one given by the nonparametric area integrand f (x;) = p 1 + kk 2 , which corresponds with the time-dependent minimal surface equation. We also study the asimpto...