Boundary value problem for one evolution equation

Sherif Amirov ()
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Sherif Amirov: Karabuk University

Indian Journal of Pure and Applied Mathematics, 2017, vol. 48, issue 3, 363-367

Abstract: Abstract The aim of the paper is to investigate the boundary value problem of the evolution equation Lu = K (x,t) ut - Δu + a (x,t) u = f (x,t). The characteristic property of this type of equations is the failure of the Petrovski’s “A” condition when coefficients are constant [1]. In this case, Cauchy problem is incorrect in the sense of Hadamard. Hence in this paper, the space, guaranteeing the correctness of the boundary value problem in the sense of Hadamard, is selected by adding some additional conditions to the coefficients of the equation.

Keywords: Evolution equations; boundary value problem; parabolic equations changing with direction of time; Sobolev type differential equations (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s13226-017-0236-5

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