Mixed initial-boundary value problem for the capillary wave equation
type: Item
instance of: scholarly article
title: Mixed initial-boundary value problem for the capillary wave equation
zbMATH Open document ID: 1347.35082
DOI: 10.1155/2016/7475061
published in: Advances in Mathematical Physics
publication date: 2016-09-08T00:00:00Z
review text: Summary: We study the mixed initial-boundary value problem for the capillary wave equation: \(i u_t +| u|^2 u =| \partial_x|^{3/2} u\), \(t>0\), \(x>0\); \(u(x, 0)=u_0(x)\), \(x>0\); \(u(0,t)+\beta u_x(0,t)=h(t)\), \(t > 0\), where \(| \partial_x|^{3 / 2} u = (1 / \sqrt{2 \pi}) \int_0^\infty\left(\operatorname{sign}(x-y)/\sqrt{| x - y|}\right) u_{y y}(y)\;dy\). 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.
Mathematics Subject Classification ID: 35F31
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 6625305
zbMATH Keywords: one space dimension
zbMATH Keywords: inhomogeneous Robin boundary conditions
Wikidata QID: Q59122555
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/7475061
OpenAlex ID: W2461936957
cites work: Positive and maximal positive solutions of singular mixed boundary value problem
cites work: Mixed boundary value problems of thermopiezoelectricity for solids with interior cracks
cites work: Mixed boundary value problems for the Stokes system
cites work: The fractional diffusion equation
cites work: The random walk's guide to anomalous diffusion: A fractional dynamics approach
cites work: Advances in Fractional Calculus
cites work: Global Existence for Capillary Water Waves
cites work: Some physical applications of fractional Schrödinger equation
cites work: On the Cauchy problem of fractional Schrödinger equation with Hartree type nonlinearity
cites work: Space-time fractional Schrödinger equation with time-independent potentials
cites work: Time dependent solutions for a fractional Schrödinger equation with delta potentials
cites work: Nonlinear fractional Schrödinger equations in one dimension
cites work: Q4650348
cites work: Mixed initial-boundary value problem for intermediate long-wave equation
cites work: Benjamin-Ono equation on a half-line
cites work: Forced cubic Schrödinger equation with Robin boundary data: large-time asymptotics
cites work: A new unified approach to study fractional PDE equations on a half-line
author: B. Juarez Campos
author: Elena I. Kaikina
author: Hector F. Ruiz Ruiz Paredes
description: scientific article; zbMATH DE number 6625305