G. V. Demidenko, A. A. Kudryavtsev, “Boundary value problems for the Rayleigh–Bishop equation in a quarter plane”, Mathematical notes of NEFU, 2021, Volume 28, Issue 3,Pages <nobr>5

This article is cited in 2 papers

Mathematics

Boundary value problems for the Rayleigh–Bishop equation in a quarter plane

G. V. Demidenko^ab, A. A. Kudryavtsev^b

^a Sobolev Institute of Mathematics, 4 Koptyug Avenue, Novosibirsk 630090, Russia
^b Novosibirsk State University, 1 Pirogov Street, Novosibirsk 630090, Russia

Abstract: We consider initial-boundary value problems for the Rayleigh–Bishop equation in a quarter plane. It is assumed that the initial-boundary value problems satisfy the Lopatinskii condition. A unique solvability in an anisotropic Sobolev space with an exponential weight is proved and an estimate for the solution is established.

Keywords: pseudohyperbolic equation, Rayleigh–Bishop equation, initial-boundary value problem, Lopatinskii condition, Sobolev space.

UDC: 517.956.223

Received: 29.03.2021
Accepted: 26.08.2021

DOI: 10.25587/SVFU.2021.81.22.001