Global existence, asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term☆

By Zhijian Yang. 2003

82 citations recorded by the source corpus.

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.

Subfields: Control and Systems Engineering, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8f8eba624b9b09f104622a561b9b3482c75dfce6

How researchers see this paper

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In Control and Systems Engineering

1. Runzhang Xu
2. Yacheng Liu
3. Patrizia Pucci
4. Yongqiang Fu

In Mathematical Physics

1. Runzhang Xu
2. Yacheng Liu
3. Patrizia Pucci
4. Yongqiang Fu

In Statistical and Nonlinear Physics

1. Runzhang Xu
2. Yacheng Liu

Citations in the corpus

• A class of fourth order wave equations with dissipative and nonlinear strain terms (2008, background): “Therefore the results on the global existence and asymptotic behavior of solutions in [4] are generalized from”
• Fourth order wave equations with nonlinear strain and source terms (2007, background): “In [4] Yang first studied the initial boundary value problem of multidimensional form of Eq.”