# Symmetry properties of positive solutions of parabolic equations: A survey

Research output: Chapter in Book/Report/Conference proceedingChapter

15 Scopus citations

## Abstract

This survey is concerned with positive solutions of nonlinear parabolic equations. assuming that the underlying domain and the equation have certain reflectional symmetries, the presented results show how positive solutions reflect the symmetries. depending on the class of solutions considered, the symmetries for all times or asymptotic symmetries are established. several classes of problems, including fully nonlinear equations on bounded domains, quasi-linear equations on n, asymptotically symmetric equations, and cooperative parabolic systems, are examined from this point of view. applications of the symmetry results in the study of asymptotic temporal behavior of solutions are also shown.

Original language English (US) Recent Progress on Reaction-Diffusion Systems and Viscosity Solutions World Scientific Publishing Co. 170-208 39 9789812834744 9812834737, 9789812834737 https://doi.org/10.1142/9789812834744_0009 Published - Jan 1 2009

## Keywords

• Asymptotic behavior
• Moving hyperplanes
• Parabolic equations and systems
• Positive solutions
• Symmetry

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