Free boundary problems with nonlocal and local diffusions Ⅱ: Spreading-vanishing and long-time behavior

Jianping Wang; Mingxin Wang

doi:10.3934/dcdsb.2020121

Article Contents

2020, Volume 25, Issue 12: 4721-4736. Doi: 10.3934/dcdsb.2020121

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Free boundary problems with nonlocal and local diffusions Ⅱ: Spreading-vanishing and long-time behavior

Jianping Wang and
Mingxin Wang^,

School of Mathematics, Harbin Institute of Technology, Harbin 150001, China

^* Corresponding author: Mingxin Wang
^* Corresponding author: Mingxin Wang

Received: October 31, 2019

Revised: December 31, 2019

Early access: March 2020

Published: December 2020

This work is supported by NSFC Grants 11771110, 11971128

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Abstract

This is part Ⅱ of our study on the free boundary problems with nonlocal and local diffusions. In part Ⅰ, we obtained the existence, uniqueness, regularity and estimates of global solution. In part Ⅱ here, we show a spreading-vanishing dichotomy, and provide the criteria of spreading and vanishing, as well as the long time behavior of solution when spreading happens.

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Mathematics Subject Classification: Primary: 35K57, 35R09, 35R20, 35R35, 92D25.

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