TY - JOUR
T1 - Hyperbolic phase-field dynamics with memory
AU - Grasselli, Maurizio
AU - Rotstein, Horacio G.
N1 - Funding Information:
This paper was initiated while the first author was visiting the Department of Mathematics of Ohio University. There he had several valuable discussions with Sergiu Aizicovici. This paper was finalized while the second author was visiting the Dipartimento di Matematica “F. Brioschi” of the Politecnico di Milano whose hospitality is gratefully acknowledged. The first author also acknowledges the partial support received by the Italian MURST Research Project “Simmetrie, Strutture Geometriche, Evoluzione E Memoria in Equazioni a Derivate Parziali.”
PY - 2001/9/1
Y1 - 2001/9/1
N2 - We consider a non-conserved phase-field system which consists of two nonlinearly coupled hyperbolic integrodifferential equations. This model is derived from two basic assumptions: the heat flux law is of Gurtin-Pipkin type and the response of the order parameter to the variation of the free energy functional is delayed. These hypotheses might be a reasonable attempt to describe, for instance, the melt of He4 crystals. A suitable initial and boundary value problem is then associated with the system and its well-posedness is analyzed in detail.
AB - We consider a non-conserved phase-field system which consists of two nonlinearly coupled hyperbolic integrodifferential equations. This model is derived from two basic assumptions: the heat flux law is of Gurtin-Pipkin type and the response of the order parameter to the variation of the free energy functional is delayed. These hypotheses might be a reasonable attempt to describe, for instance, the melt of He4 crystals. A suitable initial and boundary value problem is then associated with the system and its well-posedness is analyzed in detail.
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U2 - 10.1006/jmaa.2001.7492
DO - 10.1006/jmaa.2001.7492
M3 - Article
AN - SCOPUS:0035457354
SN - 0022-247X
VL - 261
SP - 205
EP - 230
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -