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  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
Online ISSN 1552-4485; Print ISSN 0033-569X

Initial boundary value problem for semilinear hyperbolic equations and parabolic equations with critical initial data

Author: Xu Runzhang
Journal: Quart. Appl. Math. 68 (2010), 459-468
MSC (2000): Primary 35L05, 35K05
Published electronically: June 4, 2010
MathSciNet review: 2676971
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Abstract: We study the initial boundary value problem of semilinear hyperbolic equations $ u_{tt}-\Delta u=f(u)$ and semilinear parabolic equations $ u_{t}-\Delta u=f(u)$ with critical initial data $ E(0)=d$ (or $ J(u_0)=d$), $ I(u_0)<0$, and prove that there exist non-global solutions under classical conditions on $ f$.

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Additional Information

Xu Runzhang
Affiliation: College of Science, Harbin Engineering University, 150001, People’s Republic of China

PII: S 0033-569X(2010)01197-0
Keywords: Semilinear hyperbolic equations, semilinear parabolic equation, critical initial data, potential wells, global nonexistence
Received by editor(s): November 18, 2008
Published electronically: June 4, 2010
Article copyright: © Copyright 2010 Brown University

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