Global existence, asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term |
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Authors: | Yang Zhijian |
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Affiliation: | Department of Mathematics, Zhengzhou University, Zhengzhou 450052, People's Republic of China |
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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. |
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Keywords: | Global solution Asymptotic behavior Blowup of solutions Nonlinear wave equation Initial boundary value problem |
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