In [] Fujita showed that for positive solutions, the initial value problem (in RN) for ut= Δu+ up
with p> 1 exhibited the following behavior: If p< pc≡ 1+ 2/N, then the initial value problem …

There is an enormous amount of work in the literature about the blow-up behavior of
evolution equations. It is our intention to introduce the theory by emphasizing the methods …

В предлагаемой книге излагается общий подход к априорным оценкам решений
нелинейных уравнений и неравенств в частных производных, основанный на методе …

A general approach to critical Fujita exponents in nonlinear parabolic problems - ScienceDirect
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We study nonnegative solutions of two porous medium equations with nonlinear coupled
boundary conditions and nonnegative nontrivial compactly supported initial data. We …

This paper establishes the blowup estimate near the blowup time for the heat equation
u_t=Δu with the nonlinear boundary condition u_n=u^p on ∂Ω*0,T), where Ω is a bounded …

It is well known that inequalities are a very important tool in classical analysis. One
application of these inequalities is the theory of PDEs (Partial Differential Equations). To our …

We provide a simple method for obtaining new Liouville theorems for scaling invariant
superlinear parabolic problems with gradient structure. To illustrate the method we prove …

321 A FUJITA–TYPE THEOREM FOR THE LAPLACE EQUATION WITH A DYNAMICAL
BOUNDARY CONDITION 1. Introduction Given a nonempty open s Page 1 Acta Math. Univ …

The Blow-Up Rate for a Semilinear Parabolic System Page 1 Journal of Mathematical
Analysis and Applications 238, 468–476 (1999) Article ID jmaa.1999.6525, available online at …