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EXISTENCE OF TRAVELLING WAVES IN NON-ISOTHERMAL PHASE DYNAMICS

SHU-YI ZHANG

Department of Mathematics and Physics, Shanghai Institute of Technology, 120 Caobao Rd. Shanghai 200235, P. R. China

https://doi.org/10.1142/S0219891607001197Cited by:6 (Source: Crossref)

Abstract

We study travelling wave solutions describing non-isothermal subsonic phase transitions in a van der Waals fluid. We apply the center manifold method and establish the existence of viscosity-capillarity profiles for small viscosity, large heat conduction, and large heat capacity.

Keywords:

AMSC: Primary 35L65, Primary 35L45, Secondary 34C37, Secondary 34C30

References

N. Bedjaouiet al., Anal. Appl. (Singapore) 3(4), 419 (2005), DOI: 10.1142/S0219530505000649. Link, Google Scholar
N. Bedjaoui and P. G. LeFloch, Proc. Roy. Soc. Edinburgh Sect. A 132(3), 545 (2002), DOI: 10.1017/S0308210500001773. Crossref, Web of Science, Google Scholar
N. Bedjaoui and P. G. LeFloch, Chinese Ann. Math. Ser. B 24(1), 17 (2003), DOI: 10.1142/S0252959903000037. Link, Web of Science, Google Scholar
S. Benzoni-Gavage, Proc. Amer. Math. Soc. 127(4), 1183 (1999), DOI: 10.1090/S0002-9939-99-04719-X. Crossref, Web of Science, Google Scholar
S. Benzoni-Gavage, Nonlinear Anal. 31(1–2), 243 (1998). Crossref, Web of Science, Google Scholar
S. Benzoni-Gavage, Arch. Ration. Mech. Anal. 150(1), 23 (1999), DOI: 10.1007/s002050050179. Crossref, Web of Science, Google Scholar
H. Fan and M. Slemrod, Handbook of Mathematical Fluid Dynamics I (North-Holland, Amsterdam, 2002) pp. 373–420. Crossref, Google Scholar
M. Grinfeld, Quart. Appl. Math. 47(1), 71 (1989). Crossref, Web of Science, Google Scholar
H. Hattori, J. Differential Equations 65(2), 158 (1986), DOI: 10.1016/0022-0396(86)90031-8. Crossref, Web of Science, Google Scholar
P. D. Lax, Commun. Pure Appl. Math. 10, 537 (1957), DOI: 10.1002/cpa.3160100406. Crossref, Web of Science, Google Scholar
P. G. LeFloch, Arch. Ration. Mech. Anal. 123(2), 153 (1993), DOI: 10.1007/BF00695275. Crossref, Web of Science, Google Scholar
M. Shearer, Arch. Ration. Mech. Anal. 93(1), 45 (1986). Crossref, Web of Science, Google Scholar
M. Slemrod, Arch. Ration. Mech. Anal. 81(4), 301 (1983), DOI: 10.1007/BF00250857. Crossref, Web of Science, Google Scholar
M. Slemrod, J. Differential Equations 52(1), 1 (1984), DOI: 10.1016/0022-0396(84)90130-X. Crossref, Web of Science, Google Scholar
Y.-G. Wang and Z. Xin, Acta Math. Appl. Sin. Engl. Ser. 19(4), 529 (2003). Google Scholar
S.-Y. Zhang, Appl. Math. Lett. 20(2), 170 (2007), DOI: 10.1016/j.aml.2006.03.010. Crossref, Web of Science, Google Scholar