Arkiv för Matematik

  • Ark. Mat.
  • Volume 28, Number 1-2 (1990), 371-381.

Long time small solutions to nonlinear parabolic equations

Chen Zhimin

Full-text: Open access

Abstract

A sharp result on global small solutions to the Cauchy problem $u_t = \Delta u + f\left( {u,Du,D^2 u,u_t } \right)\left( {t > 0} \right),u\left( 0 \right) = u_0 $

In Rn is obtained under the the assumption that f is C1+r for r>2/n and ‖u0‖C2(Rn) +‖u0‖W ${}_{1}^{2}$ (Rn) is small. This implies that the assumption that f is smooth and ‖u0 ‖W ${}_{1}^{k}$ (Rn)+‖u0‖W ${}_{2}^{k}$ (Rn) is small for k large enough, made in earlier work, is unnecessary.

Article information

Source
Ark. Mat. Volume 28, Number 1-2 (1990), 371-381.

Dates
Received: 16 May 1989
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898024

Digital Object Identifier
doi:10.1007/BF02387387

Mathematical Reviews number (MathSciNet)
MR1084022

Zentralblatt MATH identifier
0733.35061

Rights
1990 © Institut Mittag-Leffler

Citation

Zhimin, Chen. Long time small solutions to nonlinear parabolic equations. Ark. Mat. 28 (1990), no. 1-2, 371--381. doi:10.1007/BF02387387. https://projecteuclid.org/euclid.afm/1485898024


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Rerefences

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