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Blow-up profiles in one-dimensional, semilinear parabolic problems

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Herrero, Miguel A. and Velázquez, J.J. L. (1992) Blow-up profiles in one-dimensional, semilinear parabolic problems. Communications in Partial Differential Equations , 17 (1-2). pp. 205-219. ISSN 0360-5302

Official URL: http://www.tandfonline.com/doi/pdf/10.1080/03605309208820839


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Abstract

Let u be a solution of the Cauchy problem ut=uxx+up, x∈R, t>0, u(x,0)=u0(x), x∈R, where p>1 and u0 is continuous, nonnegative, and bounded. Suppose that u blows up at t=T<∞ and u(x,t)≢(p−1)−1/(p−1)(T−t)−1/(p−1). The authors show that the blow-up set is discrete. Also, if x=0 is a blow-up point then either limx→0[|x|2/log|x|]1/(p−1)u(x,T)=[8p/(p−1)2] 1/(p−1) or there exists a constant C>0 and an even integer m≥4 such that limx→0|x|m/(p−1)u(x,T)=C.


Item Type:Article
Uncontrolled Keywords:Heat-equations; Cauchy problem
Subjects:Sciences > Mathematics > Differential equations
ID Code:18052
Deposited On:30 Jan 2013 09:49
Last Modified:12 Dec 2018 15:08

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