Abstract:
We study the initial-boundary value problem for a third-order mixed-type differential equation. The issues of correctness of the problem statement are considered, and the existence and uniqueness of solutions are analyzed. Theorems on the conditional stability of the solution depending on the correctness set are proved. To obtain approximate solutions, we use a regularization method based on the calculation of a priori estimates. The study uses spectral analysis, which allows us to obtain numerical solutions and evaluate their stability. The results can be useful for further research in the field of mathematical physics and computational mathematics.
Keywords:ill-posed boundary value problem, conditional stability, set of correctness, a priori estimate, spectral problem, approximate solution
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