Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON THE CONJUGATE DARBOUX-PROTTER PROBLEMS FOR THE TWO DIMENSIONAL WAVE EQUATIONS IN THE SPECIAL CASE

  • Choi, Jong-Bae (Department of Mathematics Kyung Hee University Seoul 131-701) ;
  • Park, Jong-Yeoul (Department of Mathematics Pusan National University Pusan 609-735)
  • Published : 2002.09.01
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Abstract

In the article [2], the conjugate Darboux-Protter problem Dn is formulated for the two dimensional wave equation in the class of unbounded functions and the uniqueness of solutions has been established. In this paper, we shall show the existence of solutions for the hyperbolic equations with Bessel operators in another special case.

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References

  1. Far East J. Appl. Math. v.5 no.1 On Darboux-Protter problem for the hyperbolic equations with Bessel operators J. B. Choi
  2. J. Korean Math. Soc. v.33 no.4 Protter's conjugate boundary value problems for the two dimensional wave equation J. D. Jeon;K.C. Khe
  3. Math. Zamethk Ya GU v.4 no.2 On the conjugate Darboux-Protter problem in the case of independence of the polar angle J. D. Jeon;K. C. Khe
  4. Sibirsk. Math. Zh. v.26 Nonuniqueness of the solutin of the Darboux problem for a class of degenerate hyperbolic equations K. C. Khe https://doi.org/10.1007/BF00968759
  5. Sibirsk. Math. Zh.: English transl. in Silberian J. Math. Y. v.5 K. C. Khe
  6. Far East Branch Acad. Sci. USSR Darboux-Protter problems for the two-dimensional wave equation K. C. Khe
  7. J. Rational Mech. Anal v.3 New boundary value problems for the wave equation and equations of mixed type M. H. Protter
  8. Science Record, New Series v.1 On a boundary value problem for the wave equation K. C. Tong
  9. Comptes Rendas Acad. Sci-Paris v.234 Sur le probleme de Cauchy pour l'equation de Poisson et l'equation des Ondes A. Weinstein
  10. Samma Brasiliensis Math v.3 no.7-9 The generalized radiation problem and the Euler-Poisson=Darboux equation A. Weinstein
  11. A.Weinstein, The generalized radiation problem and the Euler-Poisson-Darboux equation, Samma Brasiliensis Math. 3 (1955), no. 7–9, 125–146.

Cited by

  1. Protter-Morawetz multidimensional problems vol.278, pp.1, 2012, https://doi.org/10.1134/S0081543812060181
  2. Semi-Fredholm Solvability in the Framework of Singular Solutions for the (3+1)-D Protter-Morawetz Problem vol.2014, 2014, https://doi.org/10.1155/2014/260287
  3. Exact Asymptotic Expansion of Singular Solutions for the (2+1)-D Protter Problem vol.2012, 2012, https://doi.org/10.1155/2012/278542
  4. Asymptotic expansions of singular solutions for (3+1)-D Protter problems vol.331, pp.2, 2007, https://doi.org/10.1016/j.jmaa.2006.09.036