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Volume 38, Issue 1
Well-Posedness and Stability for Semilinear Thermoelastic System with Boundary Time-Varying Delay and Nonlinear Weight

Lingrui Zhang, Xuezhi Li & Alain Miranville

DOI: 10.4208/jpde.v38.n1.3

J. Part. Diff. Eq., 38 (2025), pp. 34-60.

Published online: 2025-04

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  • Abstract

This paper is concerned with the well-posedness, uniform asymptotic stability and dynamics for a semilinear thermoelastic system with time-varying delay boundary feedback and nonlinear weight, which can be used to describe the physical procedure of meridian retraction and release therapy. The perturbation theory of linear operators by Kato is used to deal with the invalidity of Lumper-Phillips theorem on non-autonomous PDEs operator, the multiplier approach and quasi-stability method lead to the stability and dynamics for our semilinear problem, which are also true for linear thermoelastic system without weight.

  • Keywords

Semilinear thermoelastic system, quasi-stability, time-varying delay, Kato’s perturbation method.

  • AMS Subject Headings

35B40, 35B41

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-38-34, author = {Zhang , LingruiLi , Xuezhi and Miranville , Alain}, title = {Well-Posedness and Stability for Semilinear Thermoelastic System with Boundary Time-Varying Delay and Nonlinear Weight}, journal = {Journal of Partial Differential Equations}, year = {2025}, volume = {38}, number = {1}, pages = {34--60}, abstract = {

This paper is concerned with the well-posedness, uniform asymptotic stability and dynamics for a semilinear thermoelastic system with time-varying delay boundary feedback and nonlinear weight, which can be used to describe the physical procedure of meridian retraction and release therapy. The perturbation theory of linear operators by Kato is used to deal with the invalidity of Lumper-Phillips theorem on non-autonomous PDEs operator, the multiplier approach and quasi-stability method lead to the stability and dynamics for our semilinear problem, which are also true for linear thermoelastic system without weight.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v38.n1.3}, url = {http://global-sci.org/intro/article_detail/jpde/24035.html} }
TY - JOUR T1 - Well-Posedness and Stability for Semilinear Thermoelastic System with Boundary Time-Varying Delay and Nonlinear Weight AU - Zhang , Lingrui AU - Li , Xuezhi AU - Miranville , Alain JO - Journal of Partial Differential Equations VL - 1 SP - 34 EP - 60 PY - 2025 DA - 2025/04 SN - 38 DO - http://doi.org/10.4208/jpde.v38.n1.3 UR - https://global-sci.org/intro/article_detail/jpde/24035.html KW - Semilinear thermoelastic system, quasi-stability, time-varying delay, Kato’s perturbation method. AB -

This paper is concerned with the well-posedness, uniform asymptotic stability and dynamics for a semilinear thermoelastic system with time-varying delay boundary feedback and nonlinear weight, which can be used to describe the physical procedure of meridian retraction and release therapy. The perturbation theory of linear operators by Kato is used to deal with the invalidity of Lumper-Phillips theorem on non-autonomous PDEs operator, the multiplier approach and quasi-stability method lead to the stability and dynamics for our semilinear problem, which are also true for linear thermoelastic system without weight.

Zhang , LingruiLi , Xuezhi and Miranville , Alain. (2025). Well-Posedness and Stability for Semilinear Thermoelastic System with Boundary Time-Varying Delay and Nonlinear Weight. Journal of Partial Differential Equations. 38 (1). 34-60. doi:10.4208/jpde.v38.n1.3
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