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1999 Semilinear parabolic equations with singular initial data in anisotropic weighted spaces
Hebe A. Biagioni, Lucio Cadeddu, Todor Gramchev
Differential Integral Equations 12(5): 613-636 (1999). DOI: 10.57262/die/1367255388


We consider the Cauchy problem for semilinear parabolic equations with strongly singular initial data and nonlinear terms with superlinear or sublinear growth at infinity. We show, under a certain link between the growth at infinity of the nonlinear term and the order of the maximal singularity of the initial data, existence and uniqueness theorems for local and global solutions. For this we introduce anisotropic weighted Hölder type spaces, following T. Kato in[16]. We examine the regularity up to the initial plane of these solutions.


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Hebe A. Biagioni. Lucio Cadeddu. Todor Gramchev. "Semilinear parabolic equations with singular initial data in anisotropic weighted spaces." Differential Integral Equations 12 (5) 613 - 636, 1999.


Published: 1999
First available in Project Euclid: 29 April 2013

zbMATH: 1014.35041
MathSciNet: MR1697248
Digital Object Identifier: 10.57262/die/1367255388

Primary: 35K55
Secondary: 35A20 , 35D10 , 35K15

Rights: Copyright © 1999 Khayyam Publishing, Inc.


Vol.12 • No. 5 • 1999
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