Existence and uniqueness of solutions to wave equations with nonlinear degenerate damping and source terms

• Autorzy: Barbu V. , Lasiecka I. , Rammaha A.
• Języki publikacji: EN

Abstrakty

EN

In this article we focus on the global well-posedness of the differential equation u [...] in Omega x(O, T), where j' denotes the derivative of a C1 convex and real valued function j. The interaction between degenerate damping and a source term constitutes the main challenge of the problem. Problems with non-degenerate damping (k = 0) have been studied in the literature (Georgiev and Todorova, 1994; Levine and Serrin, 1997; Vitillaro, 2003). Thus the degeneracy of monotonicity is the main novelty of this work. Depending on the level of interaction between the source and the damping we characterize the domain of the parameters p, m, k, n (see below) for which one obt ains existence, regularity or finite time blow up of solutions. More specifically, when p [is less than or equal to] m + k global existence of generalized solutions in H1 x L2 is proved. For p > m + k, solutions blow up in a finite time. Higher energy solutions are studied as well. For H2 x H1 initial data we obtain both local and global solutions with the same regularity. Higher energy solutions are also proved to be unique.

Słowa kluczowe

EN

wave equations; damping and source terms; weak solutions; subdifferential; blow-up of solutions; energy estimates

PL

równanie falowe; rozwiązania słabe

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2005
• Tom: Vol. 34, no 3
• Strony: 665--687
• Opis fizyczny: Bibliogr. 35 poz.

Twórcy

autor

Barbu V.

• Department of Mathematics, University “Al. J. Cuza” 6600 Iasi, Romania

autor

Lasiecka I.

• Department of Mathematics, University of Virginia, Charlottesville, VA 22904-4137, USA

autor

Rammaha A.

• Department of Mathematics, University of Nebraska-Lincoln Lincoln, NE 68588-0130, USA

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