Blow-up of solutions of nonlinear parabolic inequalities

Taliaferro, Steven

doi:10.1090/S0002-9947-09-04770-9

Blow-up of solutions of nonlinear parabolic inequalities
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by Steven D. Taliaferro PDF

Trans. Amer. Math. Soc. 361 (2009), 3289-3302 Request permission

Abstract:

We study nonnegative solutions $u(x,t)$ of the nonlinear parabolic inequalities \[ au^\lambda \le u_t - \Delta u \le u^\lambda \] in various subsets of $\textbf {R}^n\times \textbf {R}$, where $\lambda >\frac {n+2}{n}$ and $a\in (0,1)$ are constants. We show that changing the value of $a$ in the open interval $(0,1)$ can dramatically affect the blow-up of these solutions.

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