Differential and Integral Equations

Semilinear parabolic equations with singular initial data in anisotropic weighted spaces

Hebe A. Biagioni, Lucio Cadeddu, and Todor Gramchev

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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


Export citation