Continuous dependence on data for a solution of the quasilinear parabolic equation with a periodic boundary condition

Abstract

In this paper we consider a parabolic equation with a periodic boundary condition and we prove the stability of a solution on the data. We give a numerical example for the stability of the solution on the data.

Identifying an unknown time dependent coefficient for quasilinear parabolic equations

“…We have the following assumptions on the data of the problem (1)-(4). (1) Let the function f (x,t, u) is continuous with respect to all arguments inD × (−∞, ∞) and satisfies the following condition…”

“…The problem of identifying of a coefficient are widely for mathematical modeling of various process of physics, chemistry, ecology and industry. For surveys on the subject, we refer the reader to [1,6,5,7,2] and the references therein.…”

Solution of parabolic problem with inverse coefficient s(t) with periodic and integral conditions

“…The inverse problems are an area of great interest to many researchers [1,3,5,4]. Especially, periodic conditions are very used conditions especially in physics and engineering [2,1,3,6…”