Well-posedness of the Tricomi Problem for the Multidimensional Lavrent'ev-Bitsadze Equation

Серик Аймурзаевич Алдашев

2024

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DOI 10.70474/05m52x96
Data confidence 70 medium
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Abstract

Numerous applications in physics and engineering involve models with partial differential equations of mixed type. The theory of boundary-value problems for such equations in two dimensions has been well studied. However, the key problem of well-posedness of mixed problems for such equations in multidimensional bounded domains remains currently unsolved. This paper establishes a mixed domain in which the solution of the Tricomi problem for the multidimensional Lavrent'ev-Bitsadze equation has a unique classical solution.