Pavol Quittner Philippe Souplet Blow-up, Global Existence and Steady States Second
Edition Page 1 Birkhäuser Advanced Texts Basler Lehrbücher Pavol Quittner Philippe …

In this paper, we introduce a new method for investigating the rate and profile of blow-up of
solutions of diffusion equations with nonlocal nonlinear reaction terms. For large classes of …

In this paper, we study the blow up problem for positive solutions of parabolic and hyperbolic
problems with reaction terms of local and nonlocal type involving a variable exponent. We …

In this paper, the stability of a blow-up mechanism for a particular Keller--Segel model that
yields chemotactic aggregation is considered. It is shown using matched asymptotic …

We construct a solution to a complex nonlinear heat equation which blows up in finite time T
only at one blow-up point. We also give a sharp description of its blow-up profile. The proof …

This paper examines the dynamics of mean curvature flow as it approaches a cylindrical
singularity. We reveal the mechanism for the isolatedness of cylindrical singularities in terms …

We study simultaneous and nonsimultaneous blow-up for solutions of the following
system\left {u_t= Δ u+ u^ r+ v^ p,\v_t= Δ v+ v^ s+ u^ q, in Ω * (0, T),\right. with Dirichlet …

We consider the semilinear heat equation ut-Δ u= f (u) for a large class of non scale invariant
nonlinearities of the form f (u)= up L (u), where p> 1 is Sobolev subcritical and L is a slowly …

We are interested in the local behavior, near a quenching point, of a solution of a semilinear
heat equation with singular powerlike absorption. Using the method of Herrero and …

The gradient blowup rate of the equation ut=∆ u+|∇ u| p, where p> 2, is studied. It is shown
that the blowup rate will never match that of the self-similar variables. In the one space …