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Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 9
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Articles

Blow up and asymptotic behavior in a nondissipative nonlinear wave equation

Jorge A. Esquivel-AvilaCiencias Basicas, Universidad Autonoma Metropolitana, San Pablo 180, Col. Reynosa Tamaulipas, Mexico City02410, Mexico.Correspondence[email protected]
Pages 1963-1978 | Received 02 Nov 2012, Accepted 20 Oct 2013, Published online: 18 Nov 2013
 
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Abstract

A nonlinear wave equation without damping and with a superlinear source term is considered. Qualitative behavior of solutions is studied. In particular, the dynamics around the ground state is analyzed. Partial results for blow up, boundedness, convergence, and rates of decay to the set of nonzero equilibria as are proved. Several invariant and positive invariant sets are defined.

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