Weak solutions with unbounded variation
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- by Donald P. Ballou
- Proc. Amer. Math. Soc. 37 (1973), 181-184
- DOI: https://doi.org/10.1090/S0002-9939-1973-0328367-7
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Abstract:
To solve a quasilinear system of hyperbolic partial differential equations with given initial data, the usual procedure is to approximate the initial data, solve the resulting problems, and show that the variation of the approximating solutions is uniformly bounded. A limiting process then can be used. This paper shows that, for simple systems, the variation of the solution need not be finite.References
- James Glimm and Peter D. Lax, Decay of solutions of systems of nonlinear hyperbolic conservation laws, Memoirs of the American Mathematical Society, No. 101, American Mathematical Society, Providence, RI, 1970. MR 265767
- J. A. Smoller and J. L. Johnson, Global solutions for an extended class of hyperbolic systems of conservation laws, Arch. Rational Mech. Anal. 32 (1969), 169–189. MR 236527, DOI 10.1007/BF00247508
- Lewis Leibovich, Solutions of the Riemann problem for hyperbolic systems of quasilinear equations without convexity conditions, J. Math. Anal. Appl. 45 (1974), 81–90. MR 348278, DOI 10.1016/0022-247X(74)90122-X
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 181-184
- MSC: Primary 35L60
- DOI: https://doi.org/10.1090/S0002-9939-1973-0328367-7
- MathSciNet review: 0328367