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Energy methods for quasilinear hyperbolic initial-boundary value problems. Applications to elastodynamics

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References

  1. Adams, R. A., Sobolev Spaces, Academic Press, New York, 1975.

    Google Scholar 

  2. Courant, R., & D. Hilbert, Methods of Mathematical Physics, Vol. 2, Wiley (Inter-science), New York, 1962.

    Google Scholar 

  3. Gurtin, M. E., An Introduction to Continuum Mechanics, Academic Press, New York, 1981.

    Google Scholar 

  4. Hughes, T. J. R., T. Kato & J. E. Marsden, Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity, Arch. Rational Mech. Anal. 63, 1977, 273–294.

    Google Scholar 

  5. Kato, T., Quasi-linear equations of evolution with applications to partial differential equations, in Spectral Theory of Differential Equations, Edited by W. N. Everitt, Springer Lecture Notes in Mathematics 448 (1975), 25–70.

  6. Kato, T., Linear and quasi-linear equations of evolution of hyperbolic type, in Hyperbolicity, Edited by G. DaPrato & G. Geymonat, Centro Internazionale Matematico Estivo, II ciclo, Cortona (1976), 125–191.

    Google Scholar 

  7. Lions, J. L., & E. Magenes, Problèmes aux Limites Non Homogènes et Applications, Vols. 1 et 2, Dunod, Paris, 1968.

    Google Scholar 

  8. Morrey, C. B., Multiple Integrals in the Calculus of Variations, Springer-Verlag, Berlin, Heidelberg, New York, 1966.

    Google Scholar 

  9. Strauss, W., On continuity of functions with values in various Banach spaces, Pacific J. Math. 19 (1966), 543–551.

    Google Scholar 

  10. Chen, V. C. & W. von Wahl, Das Rand-Anfangswertproblem für quasilineare Wellenleichungen in Sobolevräumen niedriger Ordnung, J. Reine Angew. Math. 337 (1982), 77–112

    Google Scholar 

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Dedicated to Jerald L. Ericksen on the occasion of his sixtieth birthday

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Dafermos, C.M., Hrusa, W.J. Energy methods for quasilinear hyperbolic initial-boundary value problems. Applications to elastodynamics. Arch. Rational Mech. Anal. 87, 267–292 (1985). https://doi.org/10.1007/BF00250727

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