PARTIAL DIFFERENTIAL EQUATIONS AND SOME OF THE APPLICATIONS
DOI:
https://doi.org/10.29121/shodhkosh.v5.i7.2024.4972Keywords:
PDE, applications on PDE, Heat conduction in solids, Thermal management of ElectronicsAbstract [English]
This paper attempts to study the partial differential equations and some of the applications on it.Basic concepts are studied.Common PDEs in different branches,solution methods,boundary and initial conditions are studied. Application of PDEs in Heat Conduction in Solids (Diffusion Equation) and Application of PDEs in Thermal Management of Electronics (Heat Equation) are studied.Conclusions are given where ever necessary and future directions are given at the last.
References
Mizohata, S., The Theory of Partial Differential Equations, translated from the Japanese, Cambridge University Press, 1973.
Kazdan, Jerry L., Applications of Partial Differential Equations to Some Problems in Differential Geometry, Notes from Lectures in Japan, 1993.
Taylor, M. E. Partial Differential Equations, Vol. 2: Qualitative Studies of Linear Equations. New York: Springer-Verlag, 1996.
. Taylor, M. E. Partial Differential Equations, Vol. 3: Nonlinear Equations. New York: Springer-Verlag, 1996.
F. Bouchut and F. James, 1998. One-dimensional transport equations with discontinuous coefficients, Nonlinear Analysis, Theory, Methods and Applications, 32, no 7, 891-933. DOI: https://doi.org/10.1016/S0362-546X(97)00536-1
Kevorkian, J. Partial Differential Equations: Analytical Solution Techniques, 2nd ed. New York: Springer-Verlag, 2000. DOI: https://doi.org/10.1007/978-1-4757-3266-5
Al-Khaled, Kamel, 2001. Numerical study of Fisher's reaction–diffusion equation by the Sinc DOI: https://doi.org/10.1016/S0377-0427(01)00356-9
collocation method, Journal of Computational and Applied Mathematics.
P.A. Markowich and C. Sparber, 2004. Highly Oscillatory Partial Differential Equations, in: Applied Mathematics Entering the 21st Century: Invited Talks from the ICIAM 2003
Congress, James M. Hill and Ross Moore, Editors, SIAM Proceedings in Applied Mathematics 116.
William Boyce and Richard DiPrima. 2005. Elementary Differential Equations and Boundary Value Problems. John Wiley & Sons Ltd., Hoboken, N.J., eight edition.
Luis, Juan Vazquez, 2006. The Porous Medium Equation: Mathematical Theory. DOI:10.1093/acprof:oso/9780198569039.001.0001. DOI: https://doi.org/10.1093/acprof:oso/9780198569039.001.0001
De Jager, E.M. (2006). "On the origin of the Korteweg–de Vries equation". arXiv:math/0602661v1.
G. K. Vallis, Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large Scale Circulation, Cambridge University Press, Cambridge, U.K., 2006. DOI: https://doi.org/10.1017/CBO9780511790447
Chow, Lu, and Ni, Hamilton’s Ricci Flow, AMS Graduate Studies in Mathematics) December 12, 2006 Segur, Harvey, 2009. The Shallow-Water Equations. DOI: https://doi.org/10.1090/gsm/077
Dobek, Steven, 2012. Fluid Dynamics and the Navier-Stokes Equation. CMSC498A: Spring ’12 Semester
Jost, J¨ urgen, Partial Differential Equations, Springer-Verlag Graduate Texts in Mathematics, Vol. 214, 3rd Edition, 2013 DOI: https://doi.org/10.1007/978-1-4614-4809-9
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Dr. Ravi. M
This work is licensed under a Creative Commons Attribution 4.0 International License.
With the licence CC-BY, authors retain the copyright, allowing anyone to download, reuse, re-print, modify, distribute, and/or copy their contribution. The work must be properly attributed to its author.
It is not necessary to ask for further permission from the author or journal board.
This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge.
