Journal
MATHEMATISCHE NACHRICHTEN
Volume 278, Issue 11, Pages 1341-1358Publisher
WILEY-V C H VERLAG GMBH
DOI: 10.1002/mana.200310310
Keywords
nonlinear wave equation; global solution; blow-up; weighted spaces; asymptotic behavior
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In this paper we consider a nonlinear wave equation with damping and source term on the whole space. For linear damping case, we show that the solution blows up in finite time even for vanishing initial energy. The criteria to guarantee blowup of solutions with positive initial energy are established both for linear and nonlinear damping cases. Global existence and large time behavior also are discussed in this work. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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