Differential and Integral Equations
- Differential Integral Equations
- Volume 20, Number 9 (2007), 1021-1034.
On bounds for global solutions of semilinear parabolic equations with critical and subcritical Sobolev exponent
In this paper, we are concerned with the existence of $L^\infty$-global bounds for global-in-time solutions of some semilinear parabolic problems. It is well known that every global-in-time solution for the subcritical problem is globally bounded in $L^\infty$, while there exists a global solution which is not bounded in $L^\infty$ globally in time in the critical case. In this paper, we discuss the necessary and sufficient condition for the existence of $L^\infty$-global bounds, which is valid for the subcritical and the critical case in a unified way. Moreover, using our main results, we provide various examples with the critical exponent in which every global-in-time solution has an $L^\infty$-global bound.
Differential Integral Equations, Volume 20, Number 9 (2007), 1021-1034.
First available in Project Euclid: 20 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Ishiwata, Michinori. On bounds for global solutions of semilinear parabolic equations with critical and subcritical Sobolev exponent. Differential Integral Equations 20 (2007), no. 9, 1021--1034. https://projecteuclid.org/euclid.die/1356039309