Premium
Global existence and nonexistence for a nonlinear wave equation with damping and source terms
Author(s) -
Zhou Yong
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310310
Subject(s) - nonlinear system , mathematics , wave equation , space (punctuation) , energy (signal processing) , work (physics) , mathematical analysis , term (time) , energy method , physics , computer science , statistics , quantum mechanics , operating system
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. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)