Characteristic Cauchy’s problem with prehistory in the case of nonlinear differential equations in partial derivatives

Abstract

We have built a constructive method of investigation and approximate solution for nonlinear Gursa’s problem with prehistory. We have established sufficient condition of subsistence, existence of unity and constant signs solution of the investigated problem. At mathematical description to different nature process (gas sorption, the spread of moisture in the porous substances, pipes heating by a stream of hot water, drying by the airflow, etc. [1]) we often come to boundary value problems for nonlinear differential equations in partial derivatives, when not all output data are known, that is some of them need to be found from auxiliary nonlinear problems, which are mathematical models of processes that proceeded the research. These problems should be named as problems with prehistory. One approach to investigation and approximate solution to such a problem has been proposed in the current paper.