Hornbook of solving problems for mixed parabolic--hyperbolic equations
Elina L. Shishkina, Azamat V. Dzarakhohov
TL;DR
This paper investigates a boundary value problem for a mixed parabolic-hyperbolic equation, demonstrating methods to establish existence and uniqueness of regular solutions in this context.
Contribution
It provides a novel approach to proving existence and uniqueness theorems for mixed parabolic-hyperbolic boundary value problems.
Findings
Existence of regular solutions is proven.
Uniqueness of solutions is established.
Methodology for mixed type equations is developed.
Abstract
In this small paper, we study a boundary value problem for an equation of parabolic-hyperbolic type. The goal is to show how we can prove existence and uniqueness theorem for a regular solution.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · Differential Equations and Numerical Methods · Stability and Controllability of Differential Equations