Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Cavitation solutions to homogeneous van der Waals type fluids involving phase transitions

Author: Baisheng Yan
Journal: Quart. Appl. Math. 53 (1995), 721-730
MSC: Primary 35Q35; Secondary 76B99
DOI: https://doi.org/10.1090/qam/1359507
MathSciNet review: MR1359507
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, weak solutions to some special Cauchy problems involving phase transitions in $ {R^3}$ are constructed. These solutions exhibit the point singularity known as cavitation.

References [Enhancements On Off] (What's this?)

  • [1] J. M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Phil. Trans. Roy. Soc. London A 306, 557-611 (1982)
  • [2] C. M. Dafermos, Hyperbolic systems of conservation laws, in Systems of Nonlinear Partial Differential Equations (J. M. Ball, ed.), D. Reidel, Dordrecht, 1983, pp. 25-70
  • [3] R. J. DiPerna, Convergence of approximate solutions to conservation laws, Arch. Rational Mech. Anal. 82, 27-70 (1983)
  • [4] J. L. Ericksen, Equilibrium of bars, Journal of Elasticity 5, 191-201 (1975)
  • [5] J. K. Hale, Ordinary differential equations, 2nd ed., R. E. Krieger Pub. Co., 1980
  • [6] R. Hardt, D. Kinderlehrer, and F. Lin, Existence and partial regularities of static liquid crystal configurations, Comm. Math. Phys. 105, 547-570 (1986)
  • [7] R. D. James, The propagation of phase boundaries in elastic bars, Arch. Rational Mech. Anal. 73, 125-158 (1980)
  • [8] P. D. Lax, Shock waves and entropy, in Contributions to Functional Analysis (E. A. Zarantonelo, ed.), Academic Press, New York, 1976, pp. 603-634
  • [9] K. A. Pericak-Spector and S. J. Spector, Nonuniqueness for a hyperbolic system: Cavitation in nonlinear elastodynamics, Arch. Rational Mech. Anal. 101, 293-317 (1988)
  • [10] M. Slemrod, Dynamics of first order phase transitions, in Phase Transformations and Material Instabilities in Solids (M. E. Gurtin, ed.), Academic Press, New York, 1984
  • [11] J. Smoller, Shock waves and reaction-diffusion equations, Springer-Verlag, New York, Berlin, Heidelberg, 1983
  • [12] L. Wheeler, A uniqueness theorem for the displacement problem in finite elastodynamics, Arch. Rational Mech. Anal. 63, 183-189 (1976)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 35Q35, 76B99

Retrieve articles in all journals with MSC: 35Q35, 76B99

Additional Information

DOI: https://doi.org/10.1090/qam/1359507
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society