Abstract: We study the solvability of boundary value problems in cylindrical domains Q = Ω × (0, T), Ω ⊂ Rn, 0 < T < +∞, for differential equations h(t) ∂2p+1u / ∂t2p+1+ (−1)p+1 Δu + c(x, t)u = f(x, t), where p is a non-negative integer, h(t) is continuous on the segment [0, T] a function such that ϕ(t) > 0 for t ∈ (0, T), ϕ(0) ≥ 0, ϕ(T) ≥ 0, and Δ is the Laplace operator in spatial variables x1, …, xn. The main feature of the problems under study is that, despite the degeneration, the boundary manifolds are not exempt to the bearing boundary conditions. We proved the existence and uniqueness theorems of the regular solutions, those having all Sobolev generalized derivatives included in the equation. Moreover, we describes some possible enhancements and generalizations of the obtained results. © 2021 A. I. Kozhanov.

Cite: Kozhanov A.I.
Boundary value problems for third–order pseudoelliptic equations with degeneration
Математические заметки СВФУ (Mathematical Notes of NEFU). 2021. V.28. N1. P.27-36. DOI: 10.25587/SVFU.2021.85.42.003 Scopus OpenAlex

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Scopus:	2-s2.0-85106027547
OpenAlex:	W3180604023

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