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

  • Demidenko Gennadiy V., demidenk@math.nsc.ru Sobolev Institute of Mathematics, 4 Koptyug Avenue, Novosibirsk 630090, Russia; Novosibirsk State University, 1 Pirogov Street, Novosibirsk 630090, Russia
  • Kudryavtsev Aleksandr A., demidenk@math.nsc.ru Novosibirsk State University, 1 Pirogov Street, Novosibirsk 630090, Russia
Keywords: pseudohyperbolic equation, Rayleigh-Bishop equation, initial-boundary value problem, Lopatinskii condition, Sobolev space

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.

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How to Cite
Demidenko, G. and Kudryavtsev, A. (2021) “Boundary value problems for the Rayleigh-Bishop equation in a quarter plane”, Mathematical notes of NEFU, 28(3), pp. 5-18. doi: https://doi.org/10.25587/SVFU.2021.81.22.001.
Section
Mathematics