Blow-up phenomena for a reaction diffusion equation with special diffusion process
نویسندگان
چکیده
منابع مشابه
Blow-up for a reaction-diffusion equation with variable coefficient
We study the blow-up behavior for positive solutions of a reaction–diffusion equationwith nonnegative variable coefficient. When there is no stationary solution, we show that the solution blows up in finite time. Under certain conditions, we then show that any point with zero source cannot be a blow-up point. © 2012 Elsevier Ltd. All rights reserved.
متن کاملBlow-up dynamics for the aggregation equation with degenerate diffusion
We study radially symmetric finite time blow-up dynamics for the aggregation equation with degenerate diffusion ut = ∆u m − ∇ · (u ∗ ∇(K ∗ u)) in R, where the kernel K(x) is of power-law form |x|−γ . Depending on m, d, γ and the initial data, the solution exhibits three kinds of blow-up behavior: self-similar with no mass concentrated at the core, imploding shock solution and near-self-similar ...
متن کاملClassification of blow-up with nonlinear diffusion and localized reaction
We study the behaviour of nonnegative solutions of the reaction-diffusion equation ut = (u)xx + a(x)up in R× (0, T ), u(x, 0) = u0(x) in R. The model contains a porous medium diffusion term with exponent m > 1, and a localized reaction a(x)up where p > 0 and a(x) ≥ 0 is a compactly supported function. We investigate the existence and behaviour of the solutions of this problem in dependenc...
متن کاملBlow-up profiles of solutions for the exponential reaction-diffusion equation
We consider the blow-up of solutions for a semilinear reaction diffusion equation with exponential reaction term. It is know that certain solutions that can be continued beyond the blow-up time possess a nonconstant selfsimilar blow-up profile. Our aim is to find the final time blow-up profile for such solutions. The proof is based on general ideas using semigroup estimates. The same approach w...
متن کاملMultiple blow-up for a porous medium equation with reaction
The present paper is concerned with the Cauchy problem { ∂tu = ∆u + u in R × (0,∞), u(x, 0) = u0(x) ≥ 0 in R , with p,m > 1. A solution u with bounded initial data is said to blow up at a finite time T if lim supt↗T ‖u(t)‖L∞(RN ) = ∞. For N ≥ 3 we obtain, in a certain range of values of p, weak solutions which blow up at several times and become bounded in intervals between these blow-up times....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applicable Analysis
سال: 2020
ISSN: 0003-6811,1563-504X
DOI: 10.1080/00036811.2020.1792447