A priori estimates of global solutions of superlinear parabolic problems without variational structure

Pavol Quittner; Philippe Souplet

doi:10.3934/dcds.2003.9.1277

Article Contents

2003, Volume 9, Issue 5: 1277-1292. Doi: 10.3934/dcds.2003.9.1277

This issue Previous Article Generalized quasilinearization method for semilinear hyperbolic problems Next Article Bifurcation from a homoclinic orbit in partial functional differential equations

A priori estimates of global solutions of superlinear parabolic problems without variational structure

Pavol Quittner^1, and
Philippe Souplet^2,

1.
Institute of Applied Mathematics and Statistics, Comenius University, Mlynská dolina, 84248 Bratislava
2.
Département de Mathématiques, Université de Picardie, INSSET, 02109 St-Quentin

Received: November 30, 2001

Revised: January 31, 2003

Published: August 2003

Abstract Related Papers Cited by

Abstract

We consider various classes of superlinear parabolic problems, including reaction-diffusion systems and scalar reaction-diffusion equations with convective or dissipative gradient terms. For these problems we prove uniform a priori estimates for all nonnegative global solutions. The existence of an energy functional for these problems is not known, so that traditional methods for a priori estimates do not apply. We use a different approach based on scaling and Fujita-type theorems. In the case of reaction-diffusion systems, we also obtain some universal bounds, i.e. a priori estimates independent of the initial data.

Keywords:

Mathematics Subject Classification: Primary: 35B45, 35K45, 35K55.

Citation:

Article Metrics

HTML views() PDF downloads(180) Cited by(0)

A priori estimates of global solutions of superlinear parabolic problems without variational structure

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

A priori estimates of global solutions of superlinear parabolic problems without variational structure

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content