\`x^2+y_1+z_12^34\`
Advanced Search
Advanced Search
Advanced Search
This issue Previous Article Next Article
Article Contents
Article Contents
2006, Volume 5, Issue 4: 827-838. Doi: 10.3934/cpaa.2006.5.827
This issue Previous Article On the uniqueness of ground state solutions of a semilinear equation containing a weighted Laplacian Next Article Quasi-periodic solutions for 1D resonant beam equation

Convergence to stationary solutions for a parabolic-hyperbolic phase-field system

  • 1.

    Dipartimento di Matematica "F. Brioschi", Politecnico di Milano, I-20133 Milano

  • 2.

    Mathematical Institute AV ČR, Žitná 25, 115 67 Praha 1

  • 3.

    Dipartimento di Matematica "F.Casorati", Università di Pavia, Via Ferrata, 1, I-27100 Pavia

Received:  December 2005
Revised:  June 2006
Published:  December 2006
Abstract Related Papers Cited by
    Abstract
  • A parabolic-hyperbolic nonconserved phase-field model is here analyzed. This is an evolution system consisting of a parabolic equation for the relative temperature $\theta$ which is nonlinearly coupled with a semilinear damped wave equation governing the order parameter $\chi$. The latter equation is characterized by a nonlinearity $\phi(\chi)$ with cubic growth. Assuming homogeneous Dirichlet and Neumann boundary conditions for $\theta$ and $\chi$, we prove that any weak solution has an $\omega$-limit set consisting of one point only. This is achieved by means of adapting a method based on the Łojasiewicz-Simon inequality. We also obtain an estimate of the decay rate to equilibrium.
    Mathematics Subject Classification: 35B40, 35Q99, 80A22.

    Citation:
    shu

    \begin{equation} \\ \end{equation}
    • Related Papers
  • Cited by
  • Access History
  • 加载中
PDF
XML
Export Citation
SHARE
Email to a Friend

Article Metrics

HTML views() PDF downloads(68) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return
    Site map Copyright © 2023 American Institute of Mathematical Sciences