Differential and Integral Equations
- Differential Integral Equations
- Volume 12, Number 5 (1999), 613-636.
Semilinear parabolic equations with singular initial data in anisotropic weighted spaces
Hebe A. Biagioni, Lucio Cadeddu, and Todor Gramchev
Abstract
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.
Article information
Source
Differential Integral Equations, Volume 12, Number 5 (1999), 613-636.
Dates
First available in Project Euclid: 29 April 2013
Permanent link to this document
https://projecteuclid.org/euclid.die/1367255388
Mathematical Reviews number (MathSciNet)
MR1697248
Zentralblatt MATH identifier
1014.35041
Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35A20: Analytic methods, singularities 35D10 35K15: Initial value problems for second-order parabolic equations
Citation
Biagioni, Hebe A.; Cadeddu, Lucio; Gramchev, Todor. Semilinear parabolic equations with singular initial data in anisotropic weighted spaces. Differential Integral Equations 12 (1999), no. 5, 613--636. https://projecteuclid.org/euclid.die/1367255388
