Global existence and blow-up for a thermoelastic system with p-Laplacian

References

• Raposo CA, Ribeiro JO, Cattai AP. Global solution for a thermoelastic system with p-Laplacian. Appl Math Lett. 2018;86:119–125.
   Web of Science ®Google Scholar
• Chen W. Cauchy problem for thermoelastic plate equations with different damping mechanisms. Commun Math Sci. 2020;18(2):429–457.
   Web of Science ®Google Scholar
• Dafermos CM. On the existence and the asymptotic stability of solutions to the equations of linear thermoelasticity. Arch Rational Mech Anal. 1968;29:241–271.
   Web of Science ®Google Scholar
• Fatori LH, Silva MAJ, Ma TF, et al. Long-time behavior of a class of thermoelastic plates with nonlinear strain. J Differ Equ. 2015;259(9):4831–4862.
   Web of Science ®Google Scholar
• Kim JU. On the energy decay of a linear thermoelastic bar and plate. SIAM J Math Anal. 1992;23(4):889–899.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Lasiecka I, Wilke M. Maximal regularity and global existence of solutions to a quasilinear thermoelastic plate system. Discrete Cont Dyn Syst. 2013;33(11–12):5189–5202.
   Web of Science ®Google Scholar
• Lebeau G, Zuazua E. Decay rates for the three-dimensional linear system of thermoelasticity. Arch Ration Mech Anal. 1999;148(3):179–231.
   Web of Science ®Google Scholar
• Liu Y, Chen W. Asymptotic profiles of solutions for regularity-loss-type generalized thermoelastic plate equations and their applications. Z Angew Math Phys. 2020;71(2): Paper No. 55, 1–26.
   PubMed Web of Science ®Google Scholar
• Rivera JEM. Energy decay rates in linear thermoelasticity. Funk Ekv. 1992;35(1):19–30.
   Google Scholar
• Rivera JEM, Qin Y. Global existence and exponential stability in one-dimensional nonlinear thermoelasticity with thermal memory. Nonlinear Anal Theory Methods Appl. 2002;51(1):11–32.
   Web of Science ®Google Scholar
• Rivera JEM, Racke R. Smoothing properties, decay, and global existence of solutions to nonlinear coupled systems of thermoelastic type. SIAM J Math Anal. 1995;26(6):1547–1563.
   Web of Science ®Google Scholar
• Rivera JEM, Racke R. Large solutions and smoothing properties for nonlinear thermoelastic systems. J Differ Equ. 1996;127(2):454–483.
   Web of Science ®Google Scholar
• Öncü TS, Moodie TB. Asymptotic analysis of a nonlinear problem in thermoelasticity. Stud Appl Math. 1994;93(2):163–186.
   Web of Science ®Google Scholar
• Qin Y, Rivera JM. Blow-up of solutions to the Cauchy problem in nonlinear one-dimensional thermoelasticity. J Math Anal Appl. 2004;292(1):160–193.
   Web of Science ®Google Scholar
• Qin Y, Rivera JEM. Global existence and exponential stability of solutions to thermoelastic equations of hyperbolic type. J Elast. 2004;75(2):125–145.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Suzuki T, Tasaki S. Stationary solutions to a thermoelastic system on shape memory materials. Nonlinearity. 2010;23(10):2623–2656.
   Web of Science ®Google Scholar
• Yang L, Wang Y-G. Well-posedness and decay estimates for Cauchy problems of linear thermoelastic systems of type III in 3-D. Indiana Univ Math J. 2006;55(4):1333–1361.
   Web of Science ®Google Scholar
• Krasnosel'skii MA. Topological methods in the theory of nonlinear integral equations. New York: The Macmillan Co.; 1964. Translated by A. H. Armstrong; translation edited by J. Burlak, A Pergamon Press Book.
   Google Scholar
• Zheng S. Nonlinear evolution equations, Vol. 133. Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics. Boca Raton, FL: Chapman & Hall/CRC; 2004.
   Google Scholar
• Levine HA. Instability and nonexistence of global solutions to nonlinear wave equations of the form Putt=−Au+F(u). Trans Am Math Soc. 1974;192:1–21.
   Web of Science ®Google Scholar
• Coffman CV. Lyusternik–Schnirelman theory and eigenvalue problems for monotone potential operators. J Funct Anal. 1973;14:237–252.
   Google Scholar