### Abstract

The authors investigate a model for dynamic phase transitions in a van der Waals compressible fluid. As the pressure is given by a nonconvex 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 nontrivial 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. They 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.

Original language | English |
---|---|

Article number | 007 |

Pages (from-to) | 93-117 |

Number of pages | 25 |

Journal | Nonlinearity |

Volume | 6 |

Issue number | 1 |

DOIs | |

Publication status | Published - Dec 1 1993 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics

### Cite this

*Nonlinearity*,

*6*(1), 93-117. [007]. https://doi.org/10.1088/0951-7715/6/1/007

}

*Nonlinearity*, vol. 6, no. 1, 007, pp. 93-117. https://doi.org/10.1088/0951-7715/6/1/007

**Local exponential attractors for models of phase change for compressible gas dynamics.** / Eden, A.; Milani, A.; Nicolaenko, B.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Local exponential attractors for models of phase change for compressible gas dynamics

AU - Eden, A.

AU - Milani, A.

AU - Nicolaenko, B.

PY - 1993/12/1

Y1 - 1993/12/1

N2 - The authors investigate a model for dynamic phase transitions in a van der Waals compressible fluid. As the pressure is given by a nonconvex 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 nontrivial 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. They 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.

AB - The authors investigate a model for dynamic phase transitions in a van der Waals compressible fluid. As the pressure is given by a nonconvex 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 nontrivial 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. They 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.

UR - http://www.scopus.com/inward/record.url?scp=0043049052&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0043049052&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/6/1/007

DO - 10.1088/0951-7715/6/1/007

M3 - Article

VL - 6

SP - 93

EP - 117

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 1

M1 - 007

ER -