This article is cited in 5 papers

On the existence of solution of some problems for nonlinear loaded parabolic equations with Cauchy data

Igor V. Frolenkov, Maria A. Darzhaa

Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041 Russia

Abstract: Two problems are considered in this paper. First problem is the Cauchy problem for a two-dimensional loaded parabolic equation with coefficients dependent on unknown function and its derivatives. Second problem is the Cauchy problem for one-dimensional equation of the Burgers-type. The sufficient conditions of the existence of solutions of these problems in classes of smooth bounded functions are presented in the paper. The method of weak approximation is used for the purpose of obtaining the proof.

Keywords: inverse problem, direct problem, loaded equation, parabolic equation, equation of the Burgers-type, method of weak approximation.

UDC: 517.9

Received: 22.10.2013
Received in revised form: 25.12.2013
Accepted: 17.02.2014

Language: English