Moore-Gibson-Thompson equation with memory, part II: general decay of energy

By Irena Lasiecka, Xiaojun Wang. 2015

183 citations recorded by the source corpus.

We study a temporally third order (Moore-Gibson-Thompson) equation with a memory term. Previously it is known that, in non-critical regime, the global solutions exist and the energy functionals decay to zero. More precisely, it is known that the energy has exponential decay if the memory kernel decays exponentially. The current work is a generalization of the previous one (Part I) in that it allows the memory kernel to be more general and shows that the energy decays the same way as the memory kernel does, exponentially or not.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/98df9d2e2cbe057e59329053cfa5fa6f12d1a21b

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In Computational Theory and Mathematics

1. Wenhui Chen
2. Ryo Ikehata
3. A. Palmieri
4. Kenji Nishihara
5. Grozdena Todorova
6. Borislav Yordanov
7. Petronela Radu

In Control and Systems Engineering

1. Wenhui Chen
2. Ryo Ikehata
3. A. Palmieri
4. M. DʼAbbicco
5. Hiroshi Takeda
6. Kenji Nishihara
7. M. Ebert

In Mathematical Physics

1. Wenhui Chen
2. Ryo Ikehata
3. A. Palmieri
4. M. DʼAbbicco
5. Hiroshi Takeda
6. Kenji Nishihara
7. M. Ebert

Citations in the corpus

• Nonexistence of global solutions for the semilinear Moore – Gibson – Thompson equation in the conservative case (2019, methodology): “ 1. Introduction In recent years, the Moore - Gibson - Thompson (MGT) equation, a linearization of a model for wave propagation in viscous thermally relaxing fluids, has caught a lot of attention (see [29, 43, 14, 20, 19, 28, 18, 25, 35, 3, 6, 24, 7, 23, 34, 2, 5] and references therein). This model ”
• Moore–Gibson–Thompson thermoelasticity (2019, unknown): “Introduction The Moore–Gibson–Thompson (MGT) equation has received huge levels of interest in recent years and many papers have been directed to studying and understanding it (see, among others, [1-6]).”
• The Cauchy problem for the Moore-Gibson-Thompson equation in the dissipative case (2020, background): “gy being exponentially stable to the limit case τ= βwith an energy being conserved. Concerning some studies for the linear or nonlinear MGT equations, we refer interested readers to the related works [42, 54, 34, 20, 36, 35, 41, 33, 40, 49, 7, 16, 39, 17, 38, 48, 5, 1, 15, 6, 51, 47, 50, 11, 12, 4, ”