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...[mathematics]], the '''Euler–Tricomi equation''' is a [[linear]] [[partial differential equation]] useful in the study of [[transonic]] [[fluid mechanics|flow]]. ...ntial equation|parabolic]] at ''x''&nbsp;=&nbsp;0 and [[hyperbolic partial differential equation|hyperbolic]] in the half plane&nbsp;''x''&nbsp;<&nbsp;0. ...

...a [[Soviet Union|Soviet]] [[mathematician]] who worked mainly on [[partial differential equation]]s. ...ms for elliptic and parabolic [[partial differential equation|differential equations]], [[Harnack's inequality|Harnack inequalities]], and [[Phragmén–Lindelöf p ...

{{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 ...

...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== ...

...e|first=H. J.|author2=W. E. Schiesser|year=2004|title=Ordinary and Partial Differential Equation Routines in C, C++, Fortran, Java, Maple and Matlab|publisher=CRC ...itle=Convergence of method of lines approximations to partial differential equations|journal=Computing|volume=33|issue=3–4|pages=297–313|doi=10.1007/bf02242274| ...

[[Image:Parabolic coords.svg|thumb|right|384px|In green, confocal parabolae opening upwards, ...a]]s. [[Parabolic cylindrical coordinates|A three-dimensional version]] of parabolic coordinates is obtained by rotating the two-dimensional [[coordinate system ...

[[File:Parabolic_coordinates_3D.png|thumb|alt=Parabolic coordinates 3D|Parabolic coordinates 3D]] ...mensional parabolic coordinates. The coordinate surfaces of the former are parabolic cylinders, and the coordinate surfaces of the latter are ''circular'' parab ...

...inates. The red parabolic cylinder corresponds to σ=2, whereas the yellow parabolic cylinder corresponds to τ=1. The blue plane corresponds to ''z''=2. These ...] that results from projecting the two-dimensional [[parabolic coordinates|parabolic coordinate system]] in the ...

In [[mathematics]], and specifically [[partial differential equations]] (PDEs), '''d´Alembert's formula''' is the general solution to the one-dim Now we can solve this system of equations to get ...

...athematician]]. She is mainly known for her work on [[partial differential equations]].<ref>{{MacTutor|id=Borok|title=Valentina Mikhailovna Borok}}</ref> ...d the applications to the theory of systems of linear partial differential equations was found to be extraordinary and was published in a top Russian journal. T ...

{{Short description|Partial differential equations describing diffusion}} ...t of an operator|adjoint]], the Kolmogorov forward equation, are [[partial differential equation]]s (PDE) that arise in the theory of continuous-time continuous-st ...

...''strong formulation''', the solution space is constructed such that these equations or conditions are already fulfilled. ==Example 1: linear system of equations== ...

...{Cite book |last=Gilbarg |first=David |title=Elliptic partial differential equations of second order |last2=Trudinger |first2=Neil S. |date=2001 |publisher=Spri ...hi = \frac{\partial^{| \alpha |} \varphi }{\partial x_1^{\alpha_1} \cdots \partial x_n^{\alpha_n}}.</math> ...

{{Short description|Type of differential operator}} ...ry of [[partial differential equations]], '''elliptic operators''' are [[differential operator]]s that generalize the [[Laplace operator]]. They are defined by t ...

{{for|the academic journal|Numerical Methods for Partial Differential Equations}} ...48DE040E38F7098D13876F7FE02DE|work=An Introduction to Partial Differential Equations|pages=309–336|editor-last=Rubinstein|editor-first=Jacob|place=Cambridge|pub ...

...dinate surface|Coordinate surfaces]] of parabolic cylindrical coordinates. Parabolic cylinder functions occur when [[separation of variables]] is used on [[Lapl ...) with ''ν'' = 5 in the complex plane from -2-2i to 2+2i|thumb|Plot of the parabolic cylinder function ''D''_''ν''(''z'') with {{nowrap|1=''ν'' = 5}} ...

The ''' diffusion equation''' is a [[parabolic partial differential equation]]. In physics, it describes the macroscopic behavior of many micro <math display="block">\frac{\partial\phi(\mathbf{r},t)}{\partial t} = \nabla \cdot \big[ D(\phi,\mathbf{r}) \ \nabla\phi(\mathbf{r},t) \big] ...

{{Short description|Technique for solving hyperbolic partial differential equations}} {{Differential equations}} ...

{{Short description|Class of partial differential equations}} ...tics]], where they are fundamental to various fields of research such as [[differential geometry]] and [[optimal transport]]. ...

| known_for = [[Hyperbolic partial differential equation]]s<br>[[Kolmogorov–Petrovsky–Piskunov equation]]<br>[[Petrovsky la ...Union|Soviet]] [[mathematician]] working mainly in the field of [[partial differential equation]]s. He greatly contributed to the solution of [[David Hilbert|Hilb ...