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
DOI: https://doi.org/10.1090/S0033-569X-2010-01197-0
Published electronically: June 4, 2010
MathSciNet review: 2676971
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 35L05, 35K05

Retrieve articles in all journals with MSC (2000): 35L05, 35K05

Additional Information

Xu Runzhang
Affiliation: College of Science, Harbin Engineering University, 150001, People’s Republic of China
Email: xurunzh@yahoo.com.cn

DOI: https://doi.org/10.1090/S0033-569X-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

American Mathematical Society