Carpio Rodríguez, Ana María
(1993)
*Existence of backward global-solutions to nonlinear dissipative wave-equations.*
Comptes Rendus de l'Académie des Sciences. Série I. Mathématique , 316
(8).
pp. 803-808.
ISSN 0764-4442

## Abstract

Let OMEGA be a bounded smooth domain of R(n). We prove existence of global solutions, i. e. solutions defined for all t is-an-element-of R, for dissipative wave equations of the form: u''-DELTAu+\u'\p-1 u'=0 in (- infinity, infinity) x OMEGA with Dirichlet homogeneous boundary conditions, where 1 < p < infinity if n less-than-or-equal-to 2 or 1 < p less-than-or-equal-to (n + 2)/(n - 2) if n > 2. More precisely, for every solution psi (with constant sign if 1 < p < 2) of an elliptic problem we prove the existence of a solution growing like \t\(p/(p-1)) when t --> - infinity. When OMEGA is unbounded the same existence result holds for p greater-than-or-equal-to 2.

Item Type: | Article |
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Uncontrolled Keywords: | Backward global solutions; existence of global solutions; dissipative wave equations; Dirichlet homogeneous boundary conditions |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 15196 |

Deposited On: | 11 May 2012 07:44 |

Last Modified: | 08 May 2013 17:23 |

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