Symmetry properties of positive solutions of parabolic equations: A survey

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17 Scopus citations


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 languageEnglish (US)
Title of host publicationRecent Progress on Reaction-Diffusion Systems and Viscosity Solutions
PublisherWorld Scientific Publishing Co.
Number of pages39
ISBN (Electronic)9789812834744
ISBN (Print)9812834737, 9789812834737
StatePublished - Jan 1 2009

Bibliographical note

Publisher Copyright:
© World Scientific Publishing Co.2009. All rights reserved.


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


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