Differential and Integral Equations

Semilinear parabolic equations with singular initial data in anisotropic weighted spaces

Hebe A. Biagioni, Lucio Cadeddu, and Todor Gramchev

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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

Differential Integral Equations, Volume 12, Number 5 (1999), 613-636.

First available in Project Euclid: 29 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations
Secondary: 35A20: Analytic methods, singularities 35D10 35K15: Initial value problems for second-order parabolic equations


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

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