Persistence in non-autonomous quasimonotone parabolic partial functional differential equations with delay

Rafael Obaya; Ana M. Sanz

doi:10.3934/dcdsb.2018338

Article Contents

2019, Volume 24, Issue 8: 3947-3970. Doi: 10.3934/dcdsb.2018338

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Persistence in non-autonomous quasimonotone parabolic partial functional differential equations with delay

Rafael Obaya^1, , and
Ana M. Sanz^2,

1.
Departamento de Matemática Aplicada, E. Ingenierías Industriales, Universidad de Valladolid, 47011 Valladolid, Spain, IMUVA, Instituto de Investigación en Matemáticas, Universidad de Valladolid
2.
Departamento de Didáctica de las Ciencias Experimentales, Sociales y de la Matemática. Facultad de Educación de Palencia, Universidad de Valladolid, 34004 Palencia, Spain, IMUVA, Instituto de Investigación en Matemáticas, Universidad de Valladolid

^* Corresponding author
^* Corresponding author

Dedicated to Peter E. Kloeden on the occasion of his 70th birthday

Received: June 2018

Revised: August 2018

Early access: January 2019

Published: August 2019

The authors were partly supported by MINECO/FEDER grant MTM2015-66330-P, and the European Commission under project H2020-MSCA-ITN-2014 643073 CRITICS.

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Abstract

This paper provides a dynamical frame to study non-autonomous parabolic partial differential equations with finite delay. Assuming monotonicity of the linearized semiflow, conditions for the existence of a continuous separation of type Ⅱ over a minimal set are given. Then, practical criteria for the uniform or strict persistence of the systems above a minimal set are obtained.

Keywords:

Topological dynamics,
skew-product semiflows,
continuous separation,
partial functional differential equations with finite delay,
uniform and strict persistence.

Mathematics Subject Classification: 35K58, 37B55, 37C60, 37C65.

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References

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