Electron. J. Diff. Eqns., Vol. 2007(2007), No. 165, pp. 1-6.

Space dimension can prevent the blow-up of solutions for parabolic problems

Alkis S. Tersenov

In the present paper, we investigate the preventive role of space dimension for semilinear parabolic problems. Conditions guaranteeing the absence of the blow-up of the solutions are formulated.

Submitted May 16, 2007. Published November 30, 2007.
Math Subject Classifications: 35K57.
Key Words: Semilinear parabolic equations; a priori estimates; blow-up.

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Alkis S. Tersenov
Department of Mathematics, University of Crete
71409 Heraklion - Crete, Greece
email: tersenov@math.uoc.gr

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