Exponential stability and maximal attractors for a one-dimensional nonlinear thermoviscoelasticity |
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Authors: | Qin Yuming |
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Institution: |
1 Department of Applied Mathematics, College of Sciences, Donghua University, Shanghai 200051, People's Republic of China, 2 Department of Mathematics, College of Mathematics and Information Sciences, Henan University, Kaifeng 475001, People's Republic of China
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Abstract: | This paper is concerned with the global existence, exponentialstability of solutions and associated nonlinear C0-semigroupas well as the existence of maximal attractors in Hi (i = 1,2, 4) for a nonlinear one-dimensional thermoviscoelasticitydescribing a kind of solid-like material. Some new ideas andmore delicated estimates are employed to prove the global existenceand exponential stability of solutions. The important featurefor the existence of maximal attractors in Hi+ (i = 1, 2, 4)is that the metric spaces H1+, H2+ and H4+ we work with arethree incomplete metric spaces, as can be seen from the physicalconstraints, i.e. > 0 and u > 0, with and u being absolutetemperature and deformation gradient (strain). For any positiveparameters 1, 2, ..., 5 verifying some conditions, a sequenceof closed subspaces Hi Hi+ (i = 1, 2, 4) is found, and theexistence of maximal attractors in Hi (i = 1, 2, 4) is established. |
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Keywords: | global existence of solutions exponential stability absorbing set C0-semigroup maximal attractors |
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