ON A SYSTEM COUPLING TWO-CRYSTALLIZATION ALLEN-CAHN EQUATIONS AND A SINGULAR NAVIER-STOKES SYSTEM

Autor(es)

Rodolfo Calsavara, Bianca Morelli ^[1] ; Boldrini, Josee Luiz ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, FCA, BR-13484350 Limeira, SP - Brazil

^[2] Univ Estadual Campinas, IMECC, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: COMMUNICATIONS IN MATHEMATICAL SCIENCES; v. 12, n. 2, p. 257-277, 2014.
• Citações Web of Science: 0

Resumo

We present a result on existence of solutions for a system of highly nonlinear and singular partial differential equations obtained by coupling the two-crystallization Allen-Cahn equations to a singular Navier-Stokes system and a nonlinear heat equation. Such a system constitutes a phase field model for non-isothermal solidification/melting processes of certain metallic alloys for which two different kinds of crystallization are possible. In this model, the liquid phase and each one of the possible crystallization states are described by their own phase fields. The possibility of occurrence of fluid flow in a a priori unknown non-solid region is also considered, turning the model into a free-boundary value problem. (AU)

• Processo FAPESP: 10/10087-8 - Controle e decaimento para sistemas de equações diferenciais parciais
• Beneficiário: Bianca Morelli Rodolfo Calsavara
• Modalidade de apoio: Auxílio à Pesquisa - Regular