LOCAL EXPONENTIAL ATTRACTORS FOR MODELS OF PHASE-CHANGE FOR COMPRESSIBLE GAS-DYNAMICS

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Author list: EDEN A, MILANI A, NICOLAENKO B

Publisher: IOP Publishing

Place: BRISTOL

Publication year: 1993

Journal: Nonlinearity (0951-7715)

Journal acronym: NONLINEARITY

Volume number: 6

Issue number: 1

Start page: 93

End page: 117

Number of pages: 25

ISSN: 0951-7715

eISSN: 1361-6544

Languages: English-Great Britain (EN-GB)

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Abstract

We investigate a model for dynamic phase transitions in a van der Waals compressible fluid. As the pressure is given by a non-convex equation of state, which also blows up for a finite volume, the corresponding initial value problem is of mixed hyperbolic-elliptic type. Therefore, it generates non-trivial dynamics. The system of conservation laws when regularized with capillarity terms excludes the appearance of shocks but keeps most of the interesting dynamics. By introducing the appropriate Hamiltonian function, local invariant domains are constructed that avoid the blow-up and at the same time allow solutions of mixed type. We show that, even in regions of mixed type, the initial value problem exhibits finite-dimensional dynamical behaviour by establishing the existence of local attractors and of exponential attractors of finite fractal dimension.

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