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
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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.
J. M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Phil. Trans. Roy. Soc. London A 306, 557–611 (1982)
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
R. J. DiPerna, Convergence of approximate solutions to conservation laws, Arch. Rational Mech. Anal. 82, 27–70 (1983)
J. L. Ericksen, Equilibrium of bars, Journal of Elasticity 5, 191–201 (1975)
J. K. Hale, Ordinary differential equations, 2nd ed., R. E. Krieger Pub. Co., 1980
R. Hardt, D. Kinderlehrer, and F. Lin, Existence and partial regularities of static liquid crystal configurations, Comm. Math. Phys. 105, 547–570 (1986)
R. D. James, The propagation of phase boundaries in elastic bars, Arch. Rational Mech. Anal. 73, 125–158 (1980)
P. D. Lax, Shock waves and entropy, in Contributions to Functional Analysis (E. A. Zarantonelo, ed.), Academic Press, New York, 1976, pp. 603–634
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)
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
J. Smoller, Shock waves and reaction-diffusion equations, Springer-Verlag, New York, Berlin, Heidelberg, 1983
L. Wheeler, A uniqueness theorem for the displacement problem in finite elastodynamics, Arch. Rational Mech. Anal. 63, 183–189 (1976)
J. M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Phil. Trans. Roy. Soc. London A 306, 557–611 (1982)
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
R. J. DiPerna, Convergence of approximate solutions to conservation laws, Arch. Rational Mech. Anal. 82, 27–70 (1983)
J. L. Ericksen, Equilibrium of bars, Journal of Elasticity 5, 191–201 (1975)
J. K. Hale, Ordinary differential equations, 2nd ed., R. E. Krieger Pub. Co., 1980
R. Hardt, D. Kinderlehrer, and F. Lin, Existence and partial regularities of static liquid crystal configurations, Comm. Math. Phys. 105, 547–570 (1986)
R. D. James, The propagation of phase boundaries in elastic bars, Arch. Rational Mech. Anal. 73, 125–158 (1980)
P. D. Lax, Shock waves and entropy, in Contributions to Functional Analysis (E. A. Zarantonelo, ed.), Academic Press, New York, 1976, pp. 603–634
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)
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
J. Smoller, Shock waves and reaction-diffusion equations, Springer-Verlag, New York, Berlin, Heidelberg, 1983
L. Wheeler, A uniqueness theorem for the displacement problem in finite elastodynamics, Arch. Rational Mech. Anal. 63, 183–189 (1976)
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Article copyright:
© Copyright 1995
American Mathematical Society
