Mixed Initial-Boundary Value Problem for the Capillary Wave Equation

Mixed Initial-Boundary Value Problem for the Capillary Wave Equation

We study the mixed initial-boundary value problem for the capillary wave equation: iut+u2u=∂x3/2u,  t>0,  x>0;  u(x,0)=u0(x),  x>0; u(0,t)+βux(0,t)=h(t),  t>0, where ∂x3/2u=(1/2π)∫0∞sign⁡x-y/x-yuyy(y) dy. We prove the global in-time existence of solutions of IBV problem for nonlinear cap...

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Main Authors: B. Juarez Campos, Elena Kaikina, Hector F. Ruiz Paredes
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2016/7475061
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spelling doaj-3c86d48080f54997b3e88f2b1ba65c7c2021-07-02T04:32:54ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/74750617475061Mixed Initial-Boundary Value Problem for the Capillary Wave EquationB. Juarez Campos0Elena Kaikina1Hector F. Ruiz Paredes2Instituto Tecnologico de Morelia, Avenida Tecnologico No. 1500, Lomas de Santiaguito, 58120 Morelia, MICH, MexicoCentro de Ciencias Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), 58089 Morelia, MICH, MexicoInstituto Tecnologico de Morelia, Avenida Tecnologico No. 1500, Lomas de Santiaguito, 58120 Morelia, MICH, MexicoWe study the mixed initial-boundary value problem for the capillary wave equation: iut+u2u=∂x3/2u,  t>0,  x>0;  u(x,0)=u0(x),  x>0; u(0,t)+βux(0,t)=h(t),  t>0, where ∂x3/2u=(1/2π)∫0∞sign⁡x-y/x-yuyy(y) dy. We prove the global in-time existence of solutions of IBV problem for nonlinear capillary equation with inhomogeneous Robin boundary conditions. Also we are interested in the study of the asymptotic behavior of solutions.http://dx.doi.org/10.1155/2016/7475061
collection DOAJ
language English
format Article
sources DOAJ
author B. Juarez Campos
Elena Kaikina
Hector F. Ruiz Paredes
spellingShingle B. Juarez Campos
Elena Kaikina
Hector F. Ruiz Paredes
Mixed Initial-Boundary Value Problem for the Capillary Wave Equation
Advances in Mathematical Physics
author_facet B. Juarez Campos
Elena Kaikina
Hector F. Ruiz Paredes
author_sort B. Juarez Campos
title Mixed Initial-Boundary Value Problem for the Capillary Wave Equation
title_short Mixed Initial-Boundary Value Problem for the Capillary Wave Equation
title_full Mixed Initial-Boundary Value Problem for the Capillary Wave Equation
title_fullStr Mixed Initial-Boundary Value Problem for the Capillary Wave Equation
title_full_unstemmed Mixed Initial-Boundary Value Problem for the Capillary Wave Equation
title_sort mixed initial-boundary value problem for the capillary wave equation
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2016-01-01
description We study the mixed initial-boundary value problem for the capillary wave equation: iut+u2u=∂x3/2u,  t>0,  x>0;  u(x,0)=u0(x),  x>0; u(0,t)+βux(0,t)=h(t),  t>0, where ∂x3/2u=(1/2π)∫0∞sign⁡x-y/x-yuyy(y) dy. We prove the global in-time existence of solutions of IBV problem for nonlinear capillary equation with inhomogeneous Robin boundary conditions. Also we are interested in the study of the asymptotic behavior of solutions.
url http://dx.doi.org/10.1155/2016/7475061
work_keys_str_mv AT bjuarezcampos mixedinitialboundaryvalueproblemforthecapillarywaveequation
AT elenakaikina mixedinitialboundaryvalueproblemforthecapillarywaveequation
AT hectorfruizparedes mixedinitialboundaryvalueproblemforthecapillarywaveequation
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