Dynamics of Partial Differential Equations

Volume 15 (2018)

Number 1

Well-posedness for the initial-boundary-value problem for the Benney–Luke equation in a quarter plane

Pages: 1 – 43

DOI: https://dx.doi.org/10.4310/DPDE.2018.v15.n1.a1

Authors

José R. Quintero (Universidad del Valle, Cali, Colombia)

Oscar E. Escobar (Universidad del Valle, Cali, Colombia)

Abstract

We study the local and globalwell posedness for the initial-boundary-value problem associated with the Benney–Luke equation on the half line on suitable Sobolev type spaces, imposing some compatibility conditions on the initial-boundary-data. The solution mapping associated to the appropriate initial-boundary-data is Lipschitz between appropriate Banach spaces.

Keywords

Benney–Luke equation, initial-boundary-value problem, existence and uniqueness

2010 Mathematics Subject Classification

35G31, 35Q35, 74J30

Full Text (PDF format)

J. R. Quintero was supported by the Mathematics Department, Universidad del Valle (research project C.I. 71007). O. Escobar was supported by the graduate program in Mathematics (Teaching Assistant). J. Q and O. E. were supported by Colciencias (Colombia) under the research grant No. 42878.

Received 8 May 2017

Published 14 December 2017