Abstract
We study a boundary value problem for nonlinear partial differential equations of the hyperbolic type on the plain in a domain with a complex boundary. To find the missing data for the given boundary constraints, we solve a supplementary nonlinear problem. For the approximation of solutions, one constructive method is built.
Highlights
The study of processes of a different nature often leads to boundary value problems for nonlinear differential equations of the hyperbolic type on the plane, defined in the domains with a complex structure of the boundary
To summarize, in the current paper, we have presented our recent results in the study of one boundary value problem for a nonlinear partial differential equation of the hyperbolic type on the plane in a domain with a complex boundary and a prehistory
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Summary
The study of processes of a different nature (e.g., gas sorption, drying by the air flow, pipes heating by a stream of hot water, etc.) often leads to boundary value problems (for short, BVPs) for nonlinear differential equations of the hyperbolic type on the plane, defined in the domains with a complex structure of the boundary. The author suggests splitting the given domain D by characteristics onto subdomains Di, i ∈ N and the consecutive solution of the classical Cauchy, Darboux, and Gaursat problems on each of these subdomains. Since it is not possible to find the exact solution of the given nonlinear problem, every following BVP will contain errors in their outcome data. It is unknown how these errors will influence the end result. This leads to the significant disadvantage of the approach, suggested by Collatz
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