한국수학사학회지 (Journal for History of Mathematics)

한국수학사학회 (The Korean Society for History of Mathematics)
권호 표지

편미분방정식 해의 공간적 감소율을 결정하는 푸앵카레 상수

  • 송종철 (한양대학교 이학부 수학전공)
  • 발행 : 2000.12.01
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초록

This paper investigates history and modern developments concerning spatial decay estimates for solutions in a semi-infinite cylinder or strip, in which model equations are defined with appropriate homogeneous lateral boundary conditions and initial conditions but left end boundary data are assumed. Our aim is to show this Saint-Venant type decay rate dependent critically on the Poincare constant resulting from characterizing variational principles.

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참고문헌

  1. SIAM J. Math. Anal. v.20 Decay estimates in steady pipe flow Ames, K.A.;L.E. Payne
  2. SIAM J. Math. Anal. v.24 Spatial decay estimates in time dependent Stokes flow Ames, K.A.;L.E. Payne;P.W. Schaefer
  3. Spatial decay in the pipe flow of a viscous fluid interfacing a porous medium Ames, K.A.;L.E. Payne;J.C. Song
  4. Proc. 3rd U.S. Nat. Cong. Appl. Mech. Some observations on Saint-Venant's principle Boley, B.A.
  5. Appl. Mech. Rev. v.42 Recent developments concerning Saint-Venant's principle: an update Horgan, C.O.
  6. Appl. Mech. Rev. v.49 Recent developments concerning Saint-Venant's principle: a second update Horgan, C.O.
  7. Arch. Rational Mech. Anal. v.68 Plane entry flows and energy estimates for the Navier-Stokes Equations Horgan, C.O.
  8. Quart. Appl. Math. v.47 Decay estimates for the biharmonic equation with applications to Saint-Venant's principle in plane elasticity and Stokes flows Horgan, C.O.
  9. Advances in Applied Mechanics v.23 Recent developments concerning Saint-Venant's principle Horgan, C.O.;J.K. Knowles;T.Y. Wu(ed.);J.W. Hutchinson(ed.)
  10. Arch. Rational Mech. Anal. v.122 Phragmen-Lindelof type results for harmonic functions with nonlinear boundary conditions Horgan, C.O.;L.E. Payne
  11. Quart. appl. Math. v.50 Saint-Venant's principle for a theory of non-linear plane elasticity Horgan, C.O.;L.E. Payne
  12. Quart. Appl. Math. v.42 Spatial decay estimates in transient heat conduction Horgan, C.O.;L.E. Payne;L.T. Wheeler
  13. SIAM J. Appl. Math. v.25 Spatial decay estimate for the Navier-Stokes equations with application to the problem of entry flow Horgan, C.O.;L.T. Wheeler
  14. Z. angew. Math. Phys.(ZAMP) v.22 On the spatial decay os solutions of the heat equation Knowles, J.K.
  15. SACCM v.2 Spatial decay estimates and energy bounds for the Stokes flow equation Lin, C.
  16. Quart. Appl. Math. v.52 Energy estimates for the biharmonic equations in three dimensions Lin, C.
  17. Math. Meth. Appl. Sci. v.21 Bounds and decay results for some second-order semilinear elliptic problems Payne, L.E.;P.W. Schaefer;J.C. Song
  18. Nonlinear Analysis v.35 Growth and decay results in heat conduction problems with nonlinear boundary conditions Payne, L.E.;P.W. Schaefer;J.C. Song
  19. SIAM J. Math. Anal. v.27 A spatial decay estimate for the hyperbolic heat equation Quintanilla, R.
  20. SIAM J. Math. Anal. v.5 Exponential decay of functionals of solutions of a peudoparabolic equation Sigillito, V.G.
  21. Z. angew. Math. Phys. (ZAMP) v.47 Phragmen-Lindelof and continuous dependence type results in generalized heat conduction Payne, L.E.;J.C. Song
  22. Continuum Mech. Thermodyn. v.9 Spatial decay estimates for the Brinkman and Darcy flows in a semi-infinite cylinder Payne, L.E.;J.C. Song
  23. Z. angew. Math. Phys. (ZAMP) Spatial decay for a model of double diffusive convection in Darcy and Brinkman flows Payne, L.E.;J.C. Song
  24. Spatial decay bounds for the Forchheimer equations Payne, L.E.;J.C. Song
  25. J. Math. Anal. Appl. v.207 Decay estimates in steady semi-infinite thermal pipe flow Song, J.C.
  26. Math. Models Meth. Appl. Sci. Spatial decay for solutions of Cauchy problems for perturbed heat equations Song, J.C.
  27. J. Korean Math. Soc. Decay estimates for steady magnetohydrodynamics equations in a semi-infinite cylinder Song, J.C.
  28. Spatial decay estimates in time-dependent double diffusive Darcy plane flow Song, J.C.
  29. J. Korean Math. Anal. v.35 Phragmen-Lindelof and continuous dependence type results in generalized dissipative heat conduction Song, J.C.;D.S. Yoon
  30. Arch. Rational Mech. Anal. v.104 Exponential decay estimates for solutions of the von Karman equations on a semi-infinite strip Vafeades, P.;C.O. Horgan