ON A NON-CORRECT PROBLEM FOR A BIHARMONIC EQUATION IN A SEMICIRCLE
Keywords:
Biharmonic equation, semicircle, non-correct problem, approximate solution, Laplace operator, conditional correctness, stability theorem, Fourier series, regularization method, Hilbert space, Fredholm equation.Abstract
Annotation: This article addresses a non-correct problem for a biharmonic equation within a semicircular domain. It explores the conditional correctness of the problem and establishes stability through a rigorous theorem. The study employs Fourier series and regularization methods, demonstrating the existence of approximate solutions despite the lack of continuous dependence on initial data. By utilizing Hilbert space concepts and Fredholm equations, the article proposes a framework for constructing reliable approximations. This work contributes to understanding complex mathematical physics problems, specifically those involving biharmonic equations in unconventional geometries.
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