On a new nonlocal boundary value problem for an equation of the mixed parabolic-hyperbolic type

Dildabek, Gulnar

doi:10.1063/1.4968471

Cited by 3 publications

(2 citation statements)

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“…They were first introduced by Nakhushev for a wave equation (see [15]). The particular case of Problem F for α + β = 2γ was considered in [3] and there the unique strong solvability of the problem is proved. x,y (Ω 1 ) ∩ C(Ω), and satisfies the inequality…”

Section: Formulation Of the Problem And Main Results On Its Solvabilitymentioning

confidence: 99%

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Unique solvability of a nonlocal problem with shift for a parabolic-hyperbolic equation

Urinov

Mamanazarov

2020

Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki

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In this article we study spectral properties of non-local boundaryvalue problem for an equation of parabolic-hyperbolic type. The non-local condition binds the solution values at points on boundaries of the parabolic and hyperbolic parts of the domain with each other. Nonlocal boundary conditions of such type are called Frankl-type conditions. This problem was first formulated by Kal'menov and Sadybekov who proved the unique strong solvability. In this article we investigate one particular case of this problem, for which we show that the problem does not have eigenvalues. 2010 Mathematics Subject Classification. 35M10, 35M12. Key words and phrases. Equation of the mixed type; parabolic-hyperbolic equation; Non-local boundary value problem; Frankl type problem; spectral properties; eigenvalues.

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Section: Formulation Of the Problem And Main Results On Its Solvabilitymentioning

confidence: 99%

“…But in our formulation of the problem the hyperbolic part coincides with a characteristic triangle. Throughout this note we mainly use techniques from our works [3,9,10,23,26,27,28] .…”

Section: Introductionmentioning

confidence: 99%