Title of article :
Global existence, asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term
Author/Authors :
Yang Zhijian، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2003
Abstract :
The paper studies the global existence, asymptotic behavior and blowup of solutions to the initial boundary value problem for a class of nonlinear wave equations with dissipative term. It proves that under rather mild conditions on nonlinear terms and initial data the above-mentioned problem admits a global weak solution and the solution decays exponentially to zero as t→+∞, respectively, in the states of large initial data and small initial energy. In particular, in the case of space dimension N=1, the weak solution is regularized to be a unique generalized solution. And if the conditions guaranteeing the global existence of weak solutions are not valid, then under the opposite conditions, the solutions of above-mentioned problem blow up in finite time. And an example is given.
Keywords :
Asymptotic behavior , Blowup of solutions , Nonlinear wave equation , Global solution , Initialboundary value problem
Journal title :
JOURNAL OF DIFFERENTIAL EQUATIONS
Journal title :
JOURNAL OF DIFFERENTIAL EQUATIONS