Parcijalna diferencijalna jednačina

Parcijalne diferencijalne jednačine:

• Linearna homogena parcijalna jednačina je oblika:

$P_{1}(x_{1},...,x_{n}){\frac {\partial u}{\partial x_{1}}}+...+P_{n}(x_{1},...,x_{n}){\frac {\partial u}{\partial x_{n}}}=0$.

• Kvazilinearna parcijalna jednačina je oblika:

$P_{1}(x_{1},...,x_{n},u){\frac {\partial u}{\partial x_{1}}}+...+P_{n}(x_{1},...,x_{n},u){\frac {\partial u}{\partial x_{n}}}=P_{n+1}(x_{1},...,x_{n},u)$.

Literatura

• Adomian, G. (1994). Solving Frontier problems of Physics: The decomposition method. Kluwer Academic Publishers. 
• Courant, R. & Hilbert, D. (1962), Methods of Mathematical Physics, II, New York: Wiley-Interscience .
• Evans, L. C. (1998), Partial Differential Equations, Providence: American Mathematical Society, ISBN 0-8218-0772-2 .
• Ibragimov, Nail H (1993), CRC Handbook of Lie Group Analysis of Differential Equations Vol. 1-3, Providence: CRC-Press, ISBN 0-8493-4488-3 .
• John, F. (1982), Partial Differential Equations (4th izd.), New York: Springer-Verlag, ISBN 0-387-90609-6 .
• Jost, J. (2002), Partial Differential Equations, New York: Springer-Verlag, ISBN 0-387-95428-7 .
• Lewy, Hans (1957), „An example of a smooth linear partial differential equation without solution”, Annals of Mathematics. Second Series 66 (1): 155–158 .
• Liao, S.J. (2003), Beyond Perturbation: Introduction to the Homotopy Analysis Method, Boca Raton: Chapman & Hall/ CRC Press, ISBN 1-58488-407-X 
• Olver, P.J. (1995), Equivalence, Invariants and Symmetry, Cambridge Press .
• Petrovskii, I. G. (1967), Partial Differential Equations, Philadelphia: W. B. Saunders Co. .
• Pinchover, Y. & Rubinstein, J. (2005), An Introduction to Partial Differential Equations, New York: Cambridge University Press, ISBN 0-521-84886-5 .
• Polyanin, A. D. (2002), Handbook of Linear Partial Differential Equations for Engineers and Scientists, Boca Raton: Chapman & Hall/CRC Press, ISBN 1-58488-299-9 .
• Polyanin, A. D. & Zaitsev, V. F. (2004), Handbook of Nonlinear Partial Differential Equations, Boca Raton: Chapman & Hall/CRC Press, ISBN 1-58488-355-3 .
• Polyanin, A. D.; Zaitsev, V. F. & Moussiaux, A. (2002), Handbook of First Order Partial Differential Equations, London: Taylor & Francis, ISBN 0-415-27267-X .
• Roubíček, T. (2013), Nonlinear Partial Differential Equations with Applications (2nd izd.), Basel, Boston, Berlin: Birkhäuser, ISBN 978-3-0348-0512-4, MR MR3014456 
• Solin, P. (2005), Partial Differential Equations and the Finite Element Method, Hoboken, NJ: J. Wiley & Sons, ISBN 0-471-72070-4 .
• Solin, P.; Segeth, K. & Dolezel, I. (2003), Higher-Order Finite Element Methods, Boca Raton: Chapman & Hall/CRC Press, ISBN 1-58488-438-X .
• Stephani, H. (1989), Differential Equations: Their Solution Using Symmetries. Edited by M. MacCallum, Cambridge University Press .
• Wazwaz, Abdul-Majid (2009). Partial Differential Equations and Solitary Waves Theory. Higher Education Press. ISBN 90-5809-369-7. 
• Zwillinger, D. (1997), Handbook of Differential Equations (3rd izd.), Boston: Academic Press, ISBN 0-12-784395-7 .
• Gershenfeld, N. (1999), The Nature of Mathematical Modeling (1st izd.), New York: Cambridge University Press, New York, NY, USA, ISBN 0-521-57095-6 .

Povezano

• Diferencijalna jednačina

Vanjske veze

Parcijalna diferencijalna jednačina na Wikimedijinoj ostavi

• Partial Differential Equations: Exact Solutions at EqWorld: The World of Mathematical Equations.
• Partial Differential Equations: Index at EqWorld: The World of Mathematical Equations.
• Partial Differential Equations: Methods at EqWorld: The World of Mathematical Equations.
• Example problems with solutions Arhivirano 2017-07-01 na Wayback Machine-u at exampleproblems.com