한국수학사학회지 (Journal for History of Mathematics)

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

열방정식 입장에서 바라본 세 방정식

  • 송종철 (한양대학교 응용수학전공)
  • 발행 : 2002.12.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This paper investigates a history of Fourier Series for the heat equation and how deeply it is related to modern famous three equations, Navier-Stokes equations in fluid dynamics, drift-diffusion equations in semiconductor, and Black-Scholes equation in finance. We also propose improved models for the heat equation with finite propagation speeds.

키워드

참고문헌

  1. Math. Models Meth. Appl. Sci. v.11 Spatial decay in the pipe flow of a viscous fluid interfacing a porous medium K.A. Ames;L.E. Payne;J.C. Song
  2. J. Math. Anal. Appl. v.185 Continuous dependence on the relaxation time and modelling, and unbounded growth, in theories of heat conduction with finite propagation speeds F. Franchi;B. Straughan
  3. Introduction to Partial Differential Equations and Hilbert Space Methods(3rd ed.) K.E. Gustafson
  4. Applicable Analysis v.38 Decay, growth, continuous dependence and uniqueness results in generalized heat conduction theories A. Morro;L.E. Payne;B. Straughan
  5. Math. Meth. Appl. Sci. v.21 Bounds and decay results for some second-order semilinear elliptic problems L.E. Payne;P.W. Schaefer;J.C. Song
  6. Nonlinear Analysis v.35 Growth and decay results in heat conduction problems with nonliner boundary conditions L.E. Payne;P.W. Schaefer;J.C. Song
  7. Z. angew. Math. Phys. (ZAMP) v.47 Phragmen-Lindelof and continuous dependence type results in generalized heat conduction L.E. Payne;J.C. Song
  8. Z. angew. Math. Phys. v.51 Spatial decay for a model of double diffusive convection in Darcy and Brinkman flows L.E. Payne;J.C. Song
  9. J. Math. Anal. Appl. v.256 Convergence results for generalized heat conduction as the relaxation time tends to zero L.E. Payne;J.C. Song
  10. International Journal of Engineering Science v.40 Growth and decay in generalized thermoelasticity L.E. Payne;J.C. Song
  11. International Journal of Engineering Science v.40 Spatial decay bounds for the Forchheimer equations L.E. Payne;J.C. Song
  12. Z. angew. Math. Phys. Spatial decay estimates for the Maxwell-Cattaneo equations with mixed boundary conditions L.E. Payne;J.C. Song
  13. Phys. Fluids v.30 A velocity-biased turbulent mixing model for passive scalars in homogeneous turbulence J.C. Song
  14. J. Math. Anal. Appl. v.207 Decay estimates in steady semi-infinite thermal pipe flow J.C. Song
  15. Math. Models Meth. Appl. Sci. v.11 Spatial decay for solutions of Cauchy problems for perturbed heat equations J.C. Song
  16. J. Math. Anal. Appl. v.267 Spatial decay estimates in time-dependent double-diffusive Darcy flow J.C. Song
  17. Nonlinear Analysis Decay estimates for Steady Magnetohydrodynamic pipe flow J.C. Song