For a single second-order elliptic partial differential equation with sufficiently smooth coefficients, all classical boundary value problems that are correct for the Laplace equations are Fredholm. The formulation of classical boundary value problems for the laplace equation is dictated by physical applications. The simplest of the boundary value problems for the Laplace equation is the Dirichlet problem, which is reduced to the problem of the field of charges distributed on a certain surface. The Dirichlet problem for partial differential equations in space is usually called the Cauchy-Dirichlet problem. This work dedicated to systems of first-order partial differential equations of elliptic and hyperbolic types consisting of four equations with three unknown variables. An explicit solution of the CauchyDirichlet problem is constructed using the method of an exponential – differential operator. Giving a very simple example of the co-solution of the Cauchy problem for a second-order differential equation and the Cauchy problem for systems of first-order hyperbolic differential equations.
THE CAUCHY-DIRICHLET PROBLEM FOR A SYSTEM OF FIRST-ORDER EQUATIONS
Published December 2020
Abstract
Language
Рус
Keywords
Elliptic and hyperbolic systems of equations
Cauchy-Dirichlet problem
exponential-differential operator
vector gradient
How to Cite
[1]
Токибетов, Ж. , Башар, .Н. and Пирманова, А. 2020. THE CAUCHY-DIRICHLET PROBLEM FOR A SYSTEM OF FIRST-ORDER EQUATIONS. Bulletin of the Abai KazNPU, the series of "Physical and Mathematical Sciences". 72, 4 (Dec. 2020), 68–72. DOI:https://doi.org/10.51889/2020-4.1728-7901.10.