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

Runzhang, Xu

doi:10.1090/S0033-569X-2010-01197-0

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
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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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