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Miranville, Alain; Quintanilla, Ramon

Some generalizations of the Caginalp phase-field system. (English) Zbl 1178.35194

Appl. Anal. 88, No. 6, 877-894 (2009).
Summary: Our aim in this article is to study generalizations of the Caginalp phase-field system based on a thermomechanical theory of deformable continua proposed by Green and Naghdi. In particular, we obtain well-posedness results and study the asymptotic and spatial behaviours of the solutions.

Cited in 33 Documents

MSC:

35K51 Initial-boundary value problems for second-order parabolic systems
35K55 Nonlinear parabolic equations
35J60 Nonlinear elliptic equations
80A22 Stefan problems, phase changes, etc.
35B40 Asymptotic behavior of solutions to PDEs
74F05 Thermal effects in solid mechanics
35Q74 PDEs in connection with mechanics of deformable solids

Keywords:

thermoelasticity; well-posedness; spatial behaviour of the solutions
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\textit{A. Miranville} and \textit{R. Quintanilla}, Appl. Anal. 88, No. 6, 877--894 (2009; Zbl 1178.35194)
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