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Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 3
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Research Article

On the existence theory for the nonlinear thermoelastic plate equation

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Pages 636-656 | Received 03 Nov 2022, Accepted 09 Apr 2023, Published online: 18 Apr 2023

References

  • Banquet C, Garbugio G, Villamizar-Roa EJ. On the existence theory for nonlinear plate equations. Z Angew Math Phys. 2022;73(1):10.
  • Boussinesq J. Théorie des ondes et de remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide dans ce canal des vitesses sensiblement de la surface au fond. J Math Pures Appl. 1872;17:55–108.
  • Banquet C, Villamizar-Roa EJ. Existence theory for the Boussinesq equation in modulation spaces. Bull Braz Math Soc (NS). 2020;51(4):1057–1082.
  • Peregrine D. Equations for water waves and the approximations behind them. In: Waves on beaches and resulting sediment transport. New York: Academic Press; 1972. p. 95–122.
  • Lasiecka I, Pokojovy M, Wan X. Global existence and exponential stability for a nonlinear thermoelastic Kirchhoff–Love plate. Nonlinear Anal Real World Appl. 2017;38:184–221.
  • Lasiecka I, Pokojovy M, Wan X. Long-time behavior of quasilinear thermoelastic Kirchhoff–Love plates with second sound. Nonlinear Anal. 2019;186:219–258.
  • Muñoz-Rivera JE, Racke R, Sepúlveda M, et al. On exponential stability for thermoelastic plates: comparison and singular limits. Appl Math Optim. 2021;84(1):1045–1081.
  • Racke R, Ueda Y. Dissipative structures for thermoelastic plate equations in Rn. Adv Differ Equ. 2016;21(7):601–630.
  • Racke R, Ueda Y. Nonlinear thermoelastic plate equations-Global existence and decay rates for the Cauchy problem. J Differ Equ. 2017;263(12):8138–8177.
  • Racke R, Ueda Y. The Cauchy problem for thermoelastic plates with two temperatures. Z Anal Anwend. 2020;39(1):103–129.
  • D'Abbicco M. The critical exponent for the dissipative plate equation with power nonlinearity. Comput Math Appl. 2017;74:1006–1014.
  • da Luz C, Charão R. Asymptotic properties for a semilinear plate equation in unbounded domains. J Hyperbolic Differ Equ. 2009;6(2):269–294.
  • Sugitani Y, Kawashima S. Decay estimates of solutions to a semi-linear dissipative plate equation. J Hyperbolic Differ Equ. 2010;7(3):471–501.

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