Asymptotic Behavior for A Class of Non-autonomous Nonclassical Parabolic Equations with Delay on Unbounded Domain

ZHANG Fang-hong, BAI Li-hong

doi:10.13371/j.cnki.chin.q.j.m.2019.04.007

Chinese Quarterly Journal of Mathematics >

2019 , Vol. 34 >Issue 4: 410 - 430

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2019.04.007

Asymptotic Behavior for A Class of Non-autonomous Nonclassical Parabolic Equations with Delay on Unbounded Domain

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1. Regional Circular Economy key Laboratory of Gansu Higher InstitutionsDepartment of Mathematics,Longqiao 2. College of Lanzhou University of Finance and EconomicsDepartment of Basic Courses,Gansu Institute of Architectural Technology

Received date: 2018-12-14

Online published: 2020-08-21

Supported by

Supported by the 2018 research funding of higher education of Gansu province project[2018B-075]

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Abstract

In this article,we investigate the longtime behavior for the following non autonomous nonclassical parabolic equations on unbounded domain u_t-△u_t-△u+λu=f（x,u（x,t-ρ（t）））+g（x,t）Under some suitable conditions on the delay term f and the non-autonomous forcing term g,we prove the existence of uniform attractors in Banach space C_H¹（R^N） for the multivalued process generated by non-autonomous nonclassical parabolic equations with delays in unbounded domain.

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ZHANG Fang-hong, BAI Li-hong . Asymptotic Behavior for A Class of Non-autonomous Nonclassical Parabolic Equations with Delay on Unbounded Domain[J]. Chinese Quarterly Journal of Mathematics, 2019 , 34(4) : 410 -430 . DOI: 10.13371/j.cnki.chin.q.j.m.2019.04.007

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