Ill-Posed Initial-Boundary Value Problem for a Third-Order Mixed Type Equation
Keywords:
stability, uniqueness, Sobolev equation, priori estimate, regularization, generalized solution, spectral problem, conditional correctnessAbstract
This paper investigates the existence and conditional stability of solutions for a initialboundary value problem related to a third-order mixed-type Sobolev equation. These types of problems arrays in various fields, including mathematical physics and fluid dynamics, as they model phenomena such as wave propagation in inhomogeneous media and filtration processes. We prove theorems of conditional correctness, another say theorems of uniqueness and conditional stability. Furthermore, the paper presents an approximate solution using regularization methods, demonstrating how to handle the instability inherent in ill-posed problems. Numerical solutions are obtained, with results shown in the form of tables and graphs. The research thus offers valuable insights into solving third-order mixed-type equations, providing a foundation for further exploration in the numerical approximation of improperly posed boundary conditions problems.
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