Wu, Hao; Grasselli, Maurizio; Zheng, Songmu Convergence to equilibrium for a parabolic-hyperbolic phase-field system with Neumann boundary conditions. (English) Zbl 1120.35024 Math. Models Methods Appl. Sci. 17, No. 1, 125-153 (2007). The paper is concerned with the asymptotic behavior of solutions to a parabolic-hyperbolic coupled system which describes the evolution of the relative temperature \(\theta\) and the order parameter \(\chi\) in a material subject to phase transitions. Neumann boundary condition for both \(\theta\) and \(\chi\) are assumed and the nonlinearities in the equation are assumed real analytic. Employing a suitable Simon-Lojasiewicz inequality the authors prove the convergence of global solutions to an equilibrium. Reviewer: Peter Poláčik (Minneapolis) Cited in 1 ReviewCited in 19 Documents MSC: 35B40 Asymptotic behavior of solutions to PDEs 80A22 Stefan problems, phase changes, etc. Keywords:Simon-Lojasiewicz inequality; real analytic nonlinearities PDFBibTeX XMLCite \textit{H. Wu} et al., Math. Models Methods Appl. Sci. 17, No. 1, 125--153 (2007; Zbl 1120.35024) Full Text: DOI References: [1] DOI: 10.1002/mma.215 · Zbl 0984.35026 [2] Aizicovici S., Dyn. Syst. Appl. 14 pp 163– [3] Aulbach B., Continuous and Discrete Dynamics Near Manifolds of Equilibria (1984) · Zbl 0535.34002 [4] DOI: 10.1007/BF01049391 · Zbl 0758.35040 [5] DOI: 10.1080/00036819108840173 · Zbl 0790.35052 [6] DOI: 10.1016/0893-9659(91)90076-8 · Zbl 0773.35028 [7] DOI: 10.1007/978-1-4612-4048-8 [8] Caginalp G., Arch. Rational Mech. Anal. 96 pp 205– [9] DOI: 10.1016/S0022-1236(02)00102-7 · Zbl 1036.26015 [10] DOI: 10.1007/978-3-0348-7301-7_4 [11] DOI: 10.3934/dcds.2004.10.211 · Zbl 1060.35011 [12] Feireisl E., Discr. Cont. Dyn. Syst. 10 pp 239– [13] DOI: 10.1023/A:1026467729263 · Zbl 0977.35069 [14] DOI: 10.1103/PhysRevE.71.046125 [15] Gatti S., Discr. Cont. Dyn. Syst. 9 pp 705– [16] Grasselli M., Adv. Math. Sci. Appl. 13 pp 443– [17] DOI: 10.3934/cpaa.2004.3.849 · Zbl 1079.35022 [18] Grasselli M., Comm. Pure Appl. Anal. 5 pp 15– [19] Haraux A., Systèmes Dynamiques Dissipatifs et Applications (1991) · Zbl 0726.58001 [20] DOI: 10.1007/s005260050133 · Zbl 0939.35122 [21] DOI: 10.1006/jfan.1997.3174 · Zbl 0895.35012 [22] DOI: 10.1006/jdeq.1997.3392 · Zbl 0912.35028 [23] Jiménez-Casas A., Rev. Mat. Complut. 15 pp 213– [24] DOI: 10.1017/S0308210500030663 · Zbl 0851.35055 [25] DOI: 10.1006/jdeq.1996.0020 · Zbl 0845.35054 [26] DOI: 10.1016/S0022-0396(02)00014-1 · Zbl 1024.35046 [27] DOI: 10.1080/03605309908821458 · Zbl 0936.35032 [28] DOI: 10.1080/03605309308820946 · Zbl 0815.35041 [29] DOI: 10.2307/2006981 · Zbl 0549.35071 [30] DOI: 10.1017/S0308210500016930 · Zbl 0414.34042 [31] DOI: 10.1016/j.jde.2004.05.004 · Zbl 1068.35018 [32] DOI: 10.1090/S0033-569X-06-01004-0 · Zbl 1120.35025 [33] DOI: 10.1007/978-1-4612-4838-5 [34] DOI: 10.3934/cpaa.2005.4.683 · Zbl 1082.35033 [35] DOI: 10.1201/9780203492222 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.