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
- Stuart S. Antman, J. L. Ericksen, David Kinderlehrer, and Ingo MΓΌller (eds.), Metastability and incompletely posed problems, The IMA Volumes in Mathematics and its Applications, vol. 3, Springer-Verlag, New York, 1987. MR 870005
- Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR 0069338
- Constantine M. Dafermos, The mixed initial-boundary value problem for the equations of nonlinear one-dimensional viscoelasticity, J. Differential Equations 6 (1969), 71β86. MR 241831, DOI https://doi.org/10.1016/0022-0396%2869%2990118-1
- R. J. DiPerna, Convergence of approximate solutions to conservation laws, Arch. Rational Mech. Anal. 82 (1983), no. 1, 27β70. MR 684413, DOI https://doi.org/10.1007/BF00251724
- Ronald J. DiPerna, Convergence of the viscosity method for isentropic gas dynamics, Comm. Math. Phys. 91 (1983), no. 1, 1β30. MR 719807
- James M. Greenberg, Richard C. MacCamy, and Victor J. Mizel, On the existence, uniqueness, and stability of solutions of the equation $\sigma ^{\prime } \,(u_{x})u_{xx}+\lambda u_{xtx}=\rho _{0}u_{tt}$, J. Math. Mech. 17 (1967/1968), 707β728. MR 0225026
- Eberhard Hopf, The partial differential equation $u_t+uu_x=\mu u_{xx}$, Comm. Pure Appl. Math. 3 (1950), 201β230. MR 47234, DOI https://doi.org/10.1002/cpa.3160030302
Ya. I. Kanelβ, On a model system of equations of one-dimensional gas motion (in Russian), Diff. Urav. 4, 721β734 (1968). Engl. transl., Diff. Eqs. 4, 374β380
- R. C. MacCamy, Existence uniqueness and stability of solutions of the equation $u_{tt}=(\partial /\partial x)(\sigma (u_{x})+\lambda (u_{x})u_{tt})$, Indiana Univ. Math. J. 20 (1970/71), 231β238. MR 265790, DOI https://doi.org/10.1512/iumj.1970.20.20021
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. MΓΌller, IMA Volumes in Mathematics and Its Applications, Vol. 3, Springer-Verlag, 1987, pp. 1β16
E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, 1955
C. M. Dafermos, The mixed initial-boundary value problem for the equations of nonlinear one-dimensional viscoelasticity, J. Diff. Eqs. 6, 71β86 (1969)
R. DiPerna, Convergence of approximate solutions to conservation laws, Arch. Rat. Mech. Anal. 82, 27β70 (1983)
R. DiPerna, Convergence of viscosity method for isentropic gas dynamics, Comm. Math. Phys. 91, 1β30 (1983)
J. M. Greenberg, R. C. MacCamy & V. J. Mizel, On the existence, uniqueness, and stability of solutions of the equation $\sigma β\left ( {{u_x}} \right ){u_{xx}} + {\lambda _{xtx}} = {\rho _0}{u_{tt}}$, J. Math. Mech. 17, 707β728 (1968)
E. Hopf, The partial differential equation ${u_t} + u{u_x} = \mu {u_{xx}}$, Comm. Pure Appl. Math. 3, 201β230 (1950)
Ya. I. Kanelβ, On a model system of equations of one-dimensional gas motion (in Russian), Diff. Urav. 4, 721β734 (1968). Engl. transl., Diff. Eqs. 4, 374β380
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, 231β238 (1970)
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
Article copyright:
© Copyright 1988
American Mathematical Society
