Open AccessThe existence and uniqueness of the global solution for the viscoelastic-plate equation under nonlinear boundary conditions
Author(s) -
Danxia Wang,
Jianwen Zhang,
Wu Run-Heng
Publication year - 2008
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.57.6741
Subject(s) - uniqueness , boundary value problem , viscoelasticity , galerkin method , mathematical analysis , nonlinear system , mathematics , boundary (topology) , weak solution , physics , thermodynamics , quantum mechanics
In this paperwe consider the viscoelastic-plate equation under non-linear boundary conditions. Firstlyby the aid of Galerkin methodunder non-linear boundary conditions (a) and the initial values w0∈Wand w1∈Wwe prove the existence and uniqueness of a global weak solution w(t) for the initial boundary value problems. Secondlyunder non-linear boundary conditions (b) and the initial values w0∈Wand w1∈W1the existence and uniqueness of a global weak solution w(t) is also proved by using Galerkin method.