Existence of backward global-solutions to nonlinear dissipative wave-equations



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Carpio, Ana (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


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
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:12 Dec 2018 15:08

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