Breakdown of smooth solutions in dissipative nonlinear hyperbolic equations

Hattori, Harumi

doi:10.1090/qam/666668

Author: Harumi Hattori
Journal: Quart. Appl. Math. 40 (1982), 113-127
MSC: Primary 35L65; Secondary 76A10
DOI: https://doi.org/10.1090/qam/666668
MathSciNet review: 666668
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B. L. Rozhdestvenskii, On the discontinuity of solutions of quasilinear equations, Amer. Math. Soc. Transl. (2) 101, 239–250 (1973)

R. L. Fosdick and G. P. MacSithigh, Shearing motions and the formation of shocks in an elastic circular tube, Quart. Appl. Math. 38 (1980/81), no. 2, 191–207. MR 580879, DOI https://doi.org/10.1090/S0033-569X-1980-0580879-X

T. Nishida, Global smooth solutions for the second-order quasilinear wave equations with the first-order dissipation (unpublished)

M. Slemrod, Instability of steady shearing flows in a nonlinear viscoelastic fluid, Arch. Rational Mech. Anal. 68 (1978), no. 3, 211–225. MR 509225, DOI https://doi.org/10.1007/BF00247740
Peter D. Lax, Development of singularities of solutions of nonlinear hyperbolic partial differential equations, J. Mathematical Phys. 5 (1964), 611–613. MR 165243, DOI https://doi.org/10.1063/1.1704154
R. C. MacCamy, A model for one-dimensional, nonlinear viscoelasticity, Quart. Appl. Math. 35 (1977/78), no. 1, 21–33. MR 478939, DOI https://doi.org/10.1090/S0033-569X-1977-0478939-6

C. M. Dafermos and J. A. Nohel, Energy methods for nonlinear hyperbolic Volterra integrodifferential equations, Univ. of Wisconsin M.R.C. Technical Summary Report No. 1876