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Forward attracting sets of reaction-diffusion equations on variable domains

  • 1Corresponding author

    1Corresponding author

Dedicated to the memory of V. S. Mel’nik.

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  • Reaction-diffusion equations on time-variable domains are instrinsically nonautonomous even if the coefficients in the equation do not depend explicitly on time. Thus the appropriate asymptotic concepts, such as attractors, are nonautonomous. Forward attracting sets based on omega-limit sets are considered in this paper. These are related to the Vishik uniform attractor but are not as restrictive since they depend only on the dynamics in the distant future. They are usually not invariant. Here it is shown that they are asymptotically positively invariant, in general, and, if the future dynamics is appropriately uniform, also asymptotically negatively invariant as well as upper semi continuous dependence in a parameter will be established. These results also apply to reaction-diffusion equations on a fixed domain.

    Mathematics Subject Classification: Primary: 37B55; Secondary: 37L30, 35K57.


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