The critical Fujita exponent for the fast diffusion equation with potential
6
TL;DR: In this paper, the authors studied the Cauchy problem for positive solutions of the fast diffusion equation with source and quadratically decaying potential in R n × (0, T ), where 1 − 2 m α + n m 1, p > 1, n ≥ 2, V ( x ) ∼ ω | x | 2 with ω ≥ 0 as | x| → ∞, and α is the positive root of m α (m α+ n − 2 ) − ω = 0 .
read more
About: This article is published in Journal of Mathematical Analysis and Applications. The article was published on 15 Feb 2013. and is currently open access.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Existence and nonexistence of global solutions for a semilinear reaction–diffusion system
TL;DR: In this paper, the blow-up and global existence of nonnegative solutions to the following Cauchy problem was studied and it was shown that m affects the Fujita critical exponent.
7
Nonexistence of solutions for the quasilinear parabolic differential inequalities with singular potential term and nonlocal source
Suping Xiao,Zhong Bo Fang +1 more
TL;DR: For a class of quasilinear parabolic differential inequalities with a singular potential term and non-local source term, this paper proved nonexistence theorems for the test function method.
The critical Fujita exponent for a diffusion equation with a potential term
TL;DR: In this article, the authors studied the initial-boundary-value problem of the diffusion equation in a conelike domain D = [1,∞) × Ω, and proved that if m < p ≤ m + 2/(n + l), then the problem has no global nonnegative solutions for any nonnegative ucffff 0 unless u>>\ 0 = 0.
5
The applications of Sobolev inequalities in proving the existence of solution of the quasilinear parabolic equation
TL;DR: In this article, the existence of global solution for the quasilinear parabolic equations was derived with the aid of some well-known inequalities, and when the blowup occurred, the lower bound of the blow-up solution was derived.
Об отсутствии слабых решений нелинейных неотрицательных параболических неравенств высокого порядка с нелокальным источником
В. Е. Адмасу
TL;DR: This paper proves the non-existence of solutions to high-order semilinear parabolic inequalities and systems with singular potential and nonlocal sources, using the test function method developed by Mitidieri and Pokhozhaev.
References
•Journal Article
The Cauchy problem for ut=Δum when 0<m<1
M. A. Herrero,M. Pierre +1 more
TL;DR: In this article, the authors consider le problem de Cauchy for l'equation de diffusion non lineaire ∂u/∂t−Δ(u|u| m−1 ) = 0 sur (0, ∞)×R N, u(0)=u 0 quand 0
151
Classification of blow-up with nonlinear diffusion and localized reaction
TL;DR: In this article, the authors studied the behavior of nonnegative solutions of the reaction diffusion equation with exponents m and p and proved that the critical exponent for global existence is p 0 = (m + 1 ) / 2, while the Fujita exponent is p c = m + 1 : if 0 p ⩽ p 0 every solution is global in time, if p 0 p ε ≥ p c all solutions blow up and if p > p c both global-in time solutions and blowing up solutions exist.
44