April  2010, 26(2): i-iii. doi: 10.3934/dcds.2010.26.2i

Preface

1. 

Department of Mathematics, University of California, Irvine, CA 92697-3875

2. 

Department of Mathematics, Vanderbilt University, Nashville, TN 37240

Published  October 2009

Nonlinear parabolic problems and applications. Nonlinear parabolic problems have long attracted the attention of the mathematical community, not least because mathematical models in several applied sciences often lead to nonlinear reaction-diffusion equations or systems. This volume is dedicated to both theoretical advances in the understanding of this broad class of problems and to the analysis of specific models of practical relevance. The 17 papers which make up the special issue can broadly be divided into two categories. One comprises papers which are mainly concerned with existence or regularity theory. Qualitative properties of solutions are the central focus of the other.
   The first paper, co-authored by Pablo Álvarez-Caudevilla and Julián López-Gómez, deals with a class of sublinear parabolic systems. A bifurcation analysis is performed which fully describes the asymptotic behavior of the system. The paper represents an important step towards a complete understanding of cooperative reaction-diffusion systems.

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Citation: Patrick Guidotti, Gieri Simonett. Preface. Discrete & Continuous Dynamical Systems, 2010, 26 (2) : i-iii. doi: 10.3934/dcds.2010.26.2i
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