Gevrey semigroup of the type III localized thermoelastic model. (English) Zbl 1510.74021
In this paper the authors consider an Euler-Bernouilli thermoelastic beam of type III (in the sense of Green and Naghdi) when the thermal effects are localized in a sub-interval of the domain determined by the beam. Boundary and transmission conditions are imposed. Existence and uniqueness of the solutions are obtained by means of the linear operator semigroup theory. The most relevant contribution of the article consists in the demonstration that the semigroup that determines the solutions is of the \(\beta\)-Gevrey (\(\beta > 8\)) type, after an interesting and beautiful mathematical analysis. Regularity of the solutions and exponential decay are two direct consequences.
Reviewer: Ramón Quintanilla De Latorre (Barcelona)
MSC:
| 74F05 | Thermal effects in solid mechanics |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74H20 | Existence of solutions of dynamical problems in solid mechanics |
| 74H25 | Uniqueness of solutions of dynamical problems in solid mechanics |
| 74H30 | Regularity of solutions of dynamical problems in solid mechanics |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
Keywords:
Euler-Bernoulli beam; type-III Green-Naghdi thermoelasticity; semigroup theory; Gevrey class; smoothing effect; existence; uniqueness; regularityReferences:
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