On the quasilinear wave equation with a mixed nonhomogeneous condition
type: Item
instance of: scholarly article
title: On the quasilinear wave equation with a mixed nonhomogeneous condition
zbMATH Open document ID: 0839.35083
author: Nguyen Thanh Long
author: Alain Pham Ngoc Dinh
published in: Southeast Asian Bulletin of Mathematics
publication date: 1995-08-07T00:00:00Z
review text: The authors consider the quasilinear wave equations \[ u_{tt}- \Delta u+ f(u_t)= 0,\;x\in (0, 1),\;t\in (0, T) \] with initial and nonhomogeneous boundary values, where \(f(u_t)= |u_t|^\alpha\text{sign}(u_t)\), \(0< \alpha< 1\). They use the Galerkin method associated with monotonic arguments to consider the global existence and the uniqueness of the solution of the aforementioned initial-boundary value problem. When the boundary condition at \(x= 0\) is linear and nonhomogeneous: \[ u_x(0, t)= h\cdot u(0, t)+ g(t),\quad h> 0, \] the behavior of the solution of the problem is considered as \(h\) tends to \(0_+\).
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 35L20
zbMATH DE Number: 773818
zbMATH Keywords: nonhomogeneous boundary condition
zbMATH Keywords: Galerkin method
reviewed by: Jinghua Wang
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 773818