No -contractive metrics for systems of conservation laws

Author:
Blake Temple

Journal:
Trans. Amer. Math. Soc. **288** (1985), 471-480

MSC:
Primary 35L65; Secondary 76L05, 76N10

MathSciNet review:
776388

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Abstract: Let

**[1]**Neal R. Amundson,*Mathematical methods in chemical engineering*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1966. Volume 1: Matrices and their application; Prentice-Hall International Series in the Physical and Chemical Engineering Sciences. MR**0371183****[2]**R. Courant and K. O. Friedricks,*Supersonic flow and shock waves*, Wiley, New York, 1948.**[3]**James Glimm,*Solutions in the large for nonlinear hyperbolic systems of equations*, Comm. Pure Appl. Math.**18**(1965), 697–715. MR**0194770****[4]**E. Isaacson,*Global solution of a Riemann problem for a non-strictly hyperbolic system of conservation laws arising in enhanced oil recovery*, J. Comp. Phys. (to appear).**[5]**F. Helfferich and G. Klein,*Multicomponent chromatography*, Dekker, New York, 1970.**[6]**Barbara Keyfitz Quinn,*Solutions with shocks: An example of an 𝐿₁-contractive semigroup*, Comm. Pure Appl. Math.**24**(1971), 125–132. MR**0271545****[7]**Barbara L. Keyfitz and Herbert C. Kranzer,*A system of nonstrictly hyperbolic conservation laws arising in elasticity theory*, Arch. Rational Mech. Anal.**72**(1979/80), no. 3, 219–241. MR**549642**, 10.1007/BF00281590**[8]**P. D. Lax,*Hyperbolic systems of conservation laws. II*, Comm. Pure Appl. Math.**10**(1957), 537–566. MR**0093653****[9]**Peter Lax,*Shock waves and entropy*, Contributions to nonlinear functional analysis (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1971) Academic Press, New York, 1971, pp. 603–634. MR**0393870****[10]**T. P. Liu and C. H. Wang,*On a hyperbolic system of conservation laws which is not strictly hyperbolic*, MRC Technical Summary Report # 2184, December 29, 1980.**[11]**D. W. Peaceman,*Fundamentals of numerical reservoir simulation*, Elsevier North-Holland, New York, 1977.**[12]**H. Rhee, R. Aris and N. R. Amundson,*On the theory of multicomponent chromatography*, Philos. Trans. Roy. Soc. London Ser. A**267**(1970), 419.**[13]**Blake Temple,*Global solution of the Cauchy problem for a class of 2×2 nonstrictly hyperbolic conservation laws*, Adv. in Appl. Math.**3**(1982), no. 3, 335–375. MR**673246**, 10.1016/S0196-8858(82)80010-9**[14]**-,*Systems of conservation laws with invariant submanifolds*, Proc. Amer. Math. Soc. (to appear).**[15]**M. Walsh, S. Bryant, R. Schechter and L. Lake,*Precipitation and dissolution of solids attending flow through porous media*, University of Texas Preprint, 1982.

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1985-0776388-5

Article copyright:
© Copyright 1985
American Mathematical Society