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Energy bounds for some non-standard problems in thermoelasticity. (English) Zbl 1145.74337
Summary: A. E. Green and P. M. Naghdi developed two theories of thermoelasticity, called type II and type III, which are likely to be more natural candidates for the identification of a thermoelastic body than the usual theory. We here derive energy bounds for a class of problem in which the ’initial data’ are given as a combination of data at time \(t=0\) and at a later time \(t=T\). Such problems are in vogue in the mathematical literature and may be used, for example, to give estimates of solution behaviour in an improperly posed problem where one wishes to continue a solution backward in time.

MSC:
74F05 Thermal effects in solid mechanics
35B45 A priori estimates in context of PDEs
35Q72 Other PDE from mechanics (MSC2000)
74B20 Nonlinear elasticity
74H55 Stability of dynamical problems in solid mechanics
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