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Zbl 0934.35101
Vitillaro, Enzo
Global nonexistence theorems for a class of evolution equations with dissipation.
(English)
[J] Arch. Ration. Mech. Anal. 149, No.2, 155-182 (1999). ISSN 0003-9527; ISSN 1432-0673/e

The paper deals with the problem of non-continuation for a solution of the abstract evolution equation $[P(u'(t))]'+A(u(t))+Q(t,u'(t))=F(u(t))$, $t\in (0,T),$ satisfying given initial data, where $A,F,P$ and $Q$ are nonlinear operators on appropriate Banach spaces. Under specific assumptions on these operators, the author proves, that the solution cannot exist for all time in the case of certain initial data. The results are applicable to important dynamical problems of nonlinear equations of elasticity with nonlinear damping.
[Marie Kopáčková (Praha)]
MSC 2000:
*35L90 Abstract hyperbolic evolution equations
35B60 Continuation of solutions of PDE
35L70 Second order nonlinear hyperbolic equations

Keywords: non-continuation of a solution; abstract evolution equation; equations of elasticity with nonlinear damping; weak solution

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