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- W2289590131 abstract "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." @default.
- W2289590131 created "2016-06-24" @default.
- W2289590131 creator A5057646292 @default.
- W2289590131 date "2007-01-01" @default.
- W2289590131 modified "2023-10-13" @default.
- W2289590131 title "On bounds for global solutions of semilinear parabolic equations with critical and subcritical Sobolev exponent" @default.
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- W2289590131 doi "https://doi.org/10.57262/die/1356039309" @default.
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