An algorithm for solving an initial boundary value problem for a mixed-type equation with delayed argument
The Hellerstedt equation with delayed argument on a special domain is considered. The author has proposed a method for constructing an algorithm for calculating a regular solution to the initial boundary value problem for the model equation of the above equation \[ \operatorname {sgn}(y)|y|^m u_{xx}(x,y)+ u_{yy}(x,y)-|y|^m u(x-\tau,y)=0 \] in a special domain, here \(0< m\), \(\tau= \text{const}\). This algorithm is based on the method of integral equations and give us the recurrence formulas for calculating a regular solution to the formulated initial boundary value problem.
scientific article; zbMATH DE number 1440454