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A mixed problem for the wave equation in a time dependent domain

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Bibliography

  1. Agmon, S., A. Douglis, & L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations. Comm. Pure and Appl. Math. 12, 623–727 (1959).

    Article  MathSciNet  MATH  Google Scholar 

  2. Darboux, M., Leçons sur la théorie des surfaces, t. 4 (note 1). Paris 1896.

  3. Duff, G.F.D., A mixed problem for normal hyperbolic linear partial differential equations of second order. Can. J. Math. 9, 141–160 (1957).

    Article  MathSciNet  MATH  Google Scholar 

  4. Duff, G.F.D., Mixed problems for hyperbolic equations of general order. Can. J. Math. 11, 195–221 (1959).

    Article  MathSciNet  MATH  Google Scholar 

  5. Gårding, L., Le problème de Goursat pour l'équation des ondes. Eleventh Scand. Math. Congress, Tronheim 1949.

  6. Goursat, É., Cours d'analyse mathématique, t. 3. Paris: Gauthier-Villars 1946.

    Google Scholar 

  7. Hadamard, J., Bull. Soc. Math. Fr. 31 (1903).

  8. Lions, J.L., Equations différentielles opérationnelles. Berlin-Göttingen-Heidelberg: Springer 1961.

    Book  MATH  Google Scholar 

  9. Nirenberg, L., Remarks on strongly elliptic partial differential equations. Comm. Pure Appl. Math. 8, 647–674 (1955).

    Article  Google Scholar 

  10. Protter, M.H., A boundary value problem for the wave equation and mean value theorems. Ann. Math. Studies No. 33, 249–257 (1954).

  11. Rogak, E.D., Thesis Univ. of Mich. 1964.

  12. Sobolev, S.L., Some new problems for partial differential equations of hyperbolic type. Mat. Sbornik 11, 155–203 (1942).

    Google Scholar 

  13. Wilcox, C., Initial-boundary value problems for linear hyperbolic partial differential equations of the second order. M.R.C. Technical Summary Report No. 301, March, 1962.

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  1. Department of Mathematics, The University of British Columbia, 8, Vancouver, Canada

    Earl D. Rogak

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  1. Earl D. Rogak
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Communicated by L. Cesari

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Rogak, E.D. A mixed problem for the wave equation in a time dependent domain. Arch Rational Mech Anal 22, 24–36 (1966). https://doi.org/10.1007/BF00281243

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