Numerical identification of a coefficient in a parabolic quasilinear equation

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

Identification of a Quasilinear Parabolic Equation from Final Data

+ c(y) = u in Ω× (0, T ), assuming that the solution of an associated boundary value problem is known at the terminal time, y(x, T ), over a (probably small) subset of Ω, for each source term u. Our work can be divided into two parts. Firstly, the uniqueness of A,~b and c is proved under appropriate assumptions. Secondly, we consider a finite-dimensional optimization problem that allows for the...

Numerical identification of a Robin coefficient in parabolic problems

This paper studies a regularization approach for an inverse problem of estimating a spatially-and-temporally dependent Robin coefficient arising in the analysis of convective heat transfer. The parameter-to-state map is analyzed, especially a differentiability result is established. A regularization approach is proposed, and the properties, e.g., existence and optimality system, of the function...

Quenching Profile for a Quasilinear Parabolic Equation

where 00, Z>0, and uq(x) >0, Vx G [—1, Z]. Without loss of generality, we may assume that uq(x) is smooth and bounded above by 1 such that uo(±Z) = 1. Since uo(x) is positive, the local (in time) existence and uniqueness of a classical solution of the problem (1.1)—(1.3) are trivial (see [8]). Many results in quenching, such as single point quenching and profiles, are similar to those b...

Rational Approximation for a Quasilinear Parabolic Equation

Approximation theorems, analogous to known results for linear elliptic equations, are obtained for solutions of the heat equation. Via the Cole-Hopf transformation, this gives rise to approximation theorems for a nonlinear parabolic equation, Burgers’ equation.