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This is a '''list of partial differential equation topics'''. *[[Partial differential equation]] ...

...[nonlinear partial differential equation|nonlinear]] fifth-order [[partial differential equation]] It is the first equation in a hierarchy of [[integrable system|integrable equations]] with the [[Lax pair|Lax operator]] ...

...rential equation; see [[Partial differential equation#Linear and nonlinear equations]] ...

...nalysis]] technique used in [[computer simulation]] for solving [[ordinary differential equation]]s by converting them to [[hyperbolic equation]]s. In this way an ...t by Johns and O'Brian 1980. This is also extended to partial differential equations. ...

{{Short description|State of linear equations}} ...m".<ref>V.V. Nemytskii, V.V. Stepanov, "Qualitative theory of differential equations", Princeton Univ. Press (1960)</ref> ...

{{Short description|Type of partial differential equations}} ...equations of [[mechanics]] are hyperbolic, and so the study of hyperbolic equations is of substantial contemporary interest. The model hyperbolic equation is t ...

...fferential equation]]s. This includes [[generalized function]]s, [[pseudo-differential operator]]s, [[wave front set]]s, [[Fourier integral operator]]s, [[oscilla ...

...It implies that the two functions separately satisfy partial differential equations, and each of the two functions is then said to be a Bäcklund transformation ...erical surface from an initial such surface using a solution of a [[linear differential equation]]. Pseudospherical surfaces can be described as solutions of the [ ...

...theory]], a theorem related to the stability of solutions of differential equations near a point of equilibrium * [[Lyapunov–Malkin theorem]], a mathematical theorem detailing nonlinear stability of systems ...

...differential geometry]] and [[differential topology]]. The use of [[linear differential equation|linear]] elliptic PDEs dates at least as far back as [[Hodge theor to the use of [[nonlinear partial differential equations]] to study geometric and topological properties of spaces, such as [[subman ...

...s, an infinite number of solutions exist; and if the number of independent equations exceeds the number of unknowns, then no solutions exist. ...e number of ''free functions'' needed to specify a solution to a [[partial differential equation]]. ...

...soliton]]s, the '''Dym equation''' ('''HD''') is the third-order [[partial differential equation]] ...quation first appeared in Kruskal <ref>[[Martin Kruskal]] ''Nonlinear Wave Equations''. In [[Jürgen Moser]], editor, Dynamical Systems, Theory and Applications, ...

{{Short description|Type of nonlinear wave in physics}} In physics, a '''breather''' is a [[nonlinear]] [[wave]] in which energy concentrates in a localized and oscillatory fas ...

...occur in fields such as [[calculus]], [[Differential equation|differential equations]] and [[Riemannian geometry]]. ==Differential equations== ...

...fferent definitions of weak solution, appropriate for different classes of equations. One of the most important is based on the notion of [[distribution (mathe ...d the solutions to it are called weak solutions). Somewhat surprisingly, a differential equation may have solutions that are not [[Differentiable function|differen ...

{{Short description|Type of differential equation subject to a particular solution methodology}} {{Differential equations}} ...

| thesis_title = Non linear evolution equations in an arbitrary Banach space ...>{{cite journal|author=Rauch, Jeffrey|title=Review: ''Partial Differential Equations'', by L. C. Evans|journal=Bull. Amer. Math. Soc. (N.S.)|year=2000|volume=37 ...

...for proving existence of solutions to [[nonlinear]] [[partial differential equations]]. * D. Gilbarg, [[N. Trudinger]], ''Elliptic Partial Differential Equations of Second Order''. {{ISBN|3-540-41160-7}}. ...

...lized Harnack's inequality to solutions of elliptic or parabolic [[partial differential equation]]s. Such results can be used to show the interior [[Hölder conditi ==Elliptic partial differential equations== ...

...(ADM) for solving [[nonlinear differential equation]]s, both ordinary and partial. The method is explained, among other places, in his book ''Solving Frontie * G. Adomian: ''Nonlinear Stochastic Operator Equations'', Academic Press, 1986. {{ISBN|0-12-044375-9}} ...