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Global existence, asymptotic behavior and uniform attractors for non-autonomous thermoelastic systems

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Abstract

In this paper, we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor for a non-autonomous thermoelastic system by using the method of uniform contractive functions. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets. Moreover, we also investigate an alternative result of solutions to the semilinear thermoelastic systems by virtue of the semigroup method.

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Authors and Affiliations

  1. Department of Applied Mathematics, Donghua University, Shanghai, 201620, China

    Yu-ming Qin, Tian-hui Wei & Jia Ren

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  1. Yu-ming Qin
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  2. Tian-hui Wei
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  3. Jia Ren
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Correspondence to Yu-ming Qin.

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Supported by the National Natural Science Foundation of China (No. 11271066; 11671075) and a grant from Shanghai Municipal Eduction Commission (No. 13ZZ048).

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Qin, Ym., Wei, Th. & Ren, J. Global existence, asymptotic behavior and uniform attractors for non-autonomous thermoelastic systems. Acta Math. Appl. Sin. Engl. Ser. 32, 1015–1034 (2016). https://doi.org/10.1007/s10255-016-0623-4

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  • DOI: https://doi.org/10.1007/s10255-016-0623-4

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