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Dafermos, C. M.; Nohel, J. A.

Energy methods for nonlinear hyperbolic Volterra integrodifferential equations. (English) Zbl 0464.45009

Commun. Partial Differ. Equations 4, 219-278 (1979).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0464.45009

Cited in 1 Review
Cited in 53 Documents

MSC:

45K05 Integro-partial differential equations
45M05 Asymptotics of solutions to integral equations

Keywords:

nonlinear hyperbolic Volterra integrodifferential equations; energy methods; global existence; boundedness; asymptotic behavior; initial value problems; resolvent kernel; Banach fixed point theorem; local solution
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References:

[1] Agmon S., Elliptic Boundary Value Problems (1965)
[2] Bellman R., Differential-Difference Equations (1963) · Zbl 0105.06402 · doi:10.1063/1.3050672
[3] Greenberg J. M., J. Math. Anal. Appl. 60 pp 617– (1977) · Zbl 0375.73001 · doi:10.1016/0022-247X(77)90005-1
[4] Lax P. D., J. Math. Phys. 5 pp 611– (1964) · Zbl 0135.15101 · doi:10.1063/1.1704154
[5] Londen S. 0., Trans. her. Math. Soc. (2) (1964)
[6] Londen S. 0., J. Differential Equations · Zbl 0209.14002
[7] MacCamy R. C., Q. Appl. Math. 35 pp 1– (1977) · Zbl 0351.45018 · doi:10.1090/qam/452184
[8] MacCamy R. C., nonlinear viscoelasticity, Ibid 35 pp 21– (1977)
[9] Matsumura A., Global existence and asymptotics of the solutions of the second order quasilinear hyperbolic equations with first order dissipation · Zbl 0371.35030 · doi:10.2977/prims/1195189813
[10] Matsumura A., Energy decay of solutions of dissipative wave equations · Zbl 0387.35041 · doi:10.3792/pjaa.53.232
[11] Nishida T., Global smooth solutions for the second-order quasilinear wave equations with the first-order dissipation
[12] Nohel J. A., A forced quasilinear wave equation with dissipation. Proceedings of Equadiff IV · Zbl 0401.35074
[13] Nohel J. A., Advances in Math 22 pp 278– (1976) · Zbl 0349.45004 · doi:10.1016/0001-8708(76)90096-7
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