Global well-posedness for semilinear hyperbolic equations with dissipative term
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- Jiang, X. & Xu, R. J. Appl. Math. Comput. (2012) 38: 467. doi:10.1007/s12190-011-0491-2
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We study the initial boundary value problem of semilinear hyperbolic equations with dissipative term. By introducing a family of potential wells we derive the invariant sets and vacuum isolating of solutions. Then we prove the global existence, nonexistence and asymptotic behaviour of solutions. In particular we obtain some sharp conditions for global existence and nonexistence of solutions.