Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

A zero-dimensional shock


Author: Stuart S. Antman
Journal: Quart. Appl. Math. 46 (1988), 569-581
MSC: Primary 34C05; Secondary 70K05, 70K99, 73F99
DOI: https://doi.org/10.1090/qam/963591
MathSciNet review: 963591
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

  • [1] S. S. Antman and R. Malek-Madani, Dissipative mechanisms, in Metastability and incompletely posed problems, edited by S. S. Antman, J. L. Ericksen, D. Kinderlehrer, I. Müller, IMA Volumes in Mathematics and Its Applications, Vol. 3, Springer-Verlag, 1987, pp. 1-16 MR 870005
  • [2] E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, 1955 MR 0069338
  • [3] C. M. Dafermos, The mixed initial-boundary value problem for the equations of nonlinear one-dimensional viscoelasticity, J. Diff. Eqs. 6, 71-86 (1969) MR 0241831
  • [4] R. DiPerna, Convergence of approximate solutions to conservation laws, Arch. Rat. Mech. Anal. 82, 27-70 (1983) MR 684413
  • [5] R. DiPerna, Convergence of viscosity method for isentropic gas dynamics, Comm. Math. Phys. 91, 1-30 (1983) MR 719807
  • [6] J. M. Greenberg, R. C. MacCamy & V. J. Mizel, On the existence, uniqueness, and stability of solutions of the equation $ \sigma '\left( {{u_x}} \right){u_{xx}} + {\lambda _{xtx}} = {\rho _0}{u_{tt}}$, J. Math. Mech. 17, 707-728 (1968) MR 0225026
  • [7] E. Hopf, The partial differential equation $ {u_t} + u{u_x} = \mu {u_{xx}}$, Comm. Pure Appl. Math. 3, 201-230 (1950) MR 0047234
  • [8] Ya. I. Kanel', On a model system of equations of one-dimensional gas motion (in Russian), Diff. Urav. 4, 721-734 (1968). Engl. transl., Diff. Eqs. 4, 374-380
  • [9] R. C. MacCamy, Existence, uniqueness, and stability of $ {u_{tt}} = \frac{\partial }{{\partial x}}\left( {\sigma \left( {{u_x}} \right) + \lambda \left( {{u_x}} \right){u_{xt}}} \right)$, Indiana Univ. Math. J. 20, 231-238 (1970) MR 0265790

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 34C05, 70K05, 70K99, 73F99

Retrieve articles in all journals with MSC: 34C05, 70K05, 70K99, 73F99


Additional Information

DOI: https://doi.org/10.1090/qam/963591
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society