DOI QR코드

DOI QR Code

ON THE CONJUGATE DARBOUX-PROTTER PROBLEMS FOR THE TWO DIMENSIONAL WAVE EQUATIONS IN THE SPECIAL CASE

  • Choi, Jong-Bae ;
  • Park, Jong-Yeoul
  • 발행 : 2002.09.01

초록

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.

키워드

the conjugate Darboux-Protter problem;the hyperbolic equation with Bessel operator

참고문헌

  1. A.Weinstein, The generalized radiation problem and the Euler-Poisson-Darboux equation, Samma Brasiliensis Math. 3 (1955), no. 7–9, 125–146.
  2. Far East J. Appl. Math. v.5 no.1 On Darboux-Protter problem for the hyperbolic equations with Bessel operators J. B. Choi
  3. 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
  4. Sibirsk. Math. Zh.: English transl. in Silberian J. Math. Y. v.5 K. C. Khe
  5. Comptes Rendas Acad. Sci-Paris v.234 Sur le probleme de Cauchy pour l'equation de Poisson et l'equation des Ondes A. Weinstein
  6. Far East Branch Acad. Sci. USSR Darboux-Protter problems for the two-dimensional wave equation K. C. Khe
  7. 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
  8. Samma Brasiliensis Math v.3 no.7-9 The generalized radiation problem and the Euler-Poisson=Darboux equation A. Weinstein
  9. J. Rational Mech. Anal v.3 New boundary value problems for the wave equation and equations of mixed type M. H. Protter
  10. 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
  11. Science Record, New Series v.1 On a boundary value problem for the wave equation K. C. Tong

피인용 문헌

  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