...old_files/data/B017/B.0107380 Boundary value problem, partial differential equations
is a differential operator. However, boundary conditions of other types also occur.
11 KB (1,579 words) - 06:29, 30 May 2020
...he set of products of solutions to homogeneous linear partial differential equations. It was introduced in [[#References|[a1]]] and used in [[#References|[a2]]]
..._mw=0\text{in}D\}$ is the null-space of the formal [[Differential operator|differential operator]] $L_m$, and the equation $L_mw=0$ is understood in the distributi
8 KB (1,320 words) - 08:38, 27 April 2021
...= 141 : ~/encyclopedia/old_files/data/P071/P.0701640 Partial differential equations on a manifold
...functions in a jet bundle, which is natural because after all a (partial) differential equation is a relation between a function, its dependent variables and its
9 KB (1,406 words) - 21:26, 3 January 2021
..._files/data/M110/M.1100190 Monte\AAhCarlo methods for partial differential equations
...ms, etc. (cf. also [[Differential equation, partial|Differential equation, partial]]).
9 KB (1,338 words) - 08:01, 6 June 2020
...0107360 Boundary value problem, numerical methods for partial differential equations
...unique stable solution, whatever the terms on the right-hand sides of the equations. By stability of a difference scheme one means that its solution depends co
16 KB (2,196 words) - 05:17, 14 September 2022
...ntial equations, ordinary, approximate methods of solution of|Differential equations, ordinary, approximate methods of solution of]].
659 bytes (73 words) - 17:20, 7 February 2011
...tial equation (cf. [[Differential equation, partial|Differential equation, partial]]) that is linear with respect to the leading derivatives of the unknown fu
...partial^2u}{\partial x^2}+\frac{\partial u}{\partial y}\frac{\partial^2u}{\partial y^2}+u^2=0$$
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...sed approximation methods for solving problems connected with differential equations. This is explained by its great universality and the relative simplicity of
...<TD valign="top"> L. Lapodus, "Numerical solution of partial differential equations in science and engineering", Wiley (1982)</TD></TR>
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.../TD> <TD valign="top"> S. Mizohata, "The theory of partial differential equations" , Cambridge Univ. Press (1973) (Translated from Japanese) {{MR|0599580}
...nt, D. Hilbert, "Methods of mathematical physics. Partial differential equations" , '''2''' , Interscience (1965) (Translated from German) {{MR|0195654}}
559 bytes (69 words) - 07:56, 16 April 2023
...an extremely overloaded notion used in different contexts. Here follows a partial list of possible disambiguations.
* Hyperbolic partial differential equations
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A differential equation of the form
...the construction of a geometric theory of first-order partial differential equations. A particular case of a Monge equation is a [[Pfaffian equation|Pfaffian eq
2 KB (249 words) - 09:01, 1 August 2014
...passing through the point $M$ and its interior; for parabolic and elliptic equations, the domain of influence of the point $M$ is usually the domain of definiti
...rst order]]; [[Hyperbolic partial differential equation|Hyperbolic partial differential equation]]). For a more precise discussion of the latter case see [[#Refere
2 KB (272 words) - 21:43, 14 April 2014
of a differential equation
...artial differential equations|Boundary value problem, partial differential equations]].
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...value problem, partial differential equations]]) for partial differential equations. For example, let there be given a second-order elliptic equation
\frac{\partial ^ {2} u ( x) }{\partial x _ {i} \partial x _ {j} }
3 KB (361 words) - 05:56, 30 May 2023
For differential equations, a property of completeness for a certain set of solutions. See
* [[Ordinary differential equations, property C for]];
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...artial differential equations|Boundary value problem, partial differential equations]]). Let $ \pmb\nu = ( \nu _ {1} \dots \nu _ {n} ) $
...erator $ D = g ^ {ij} ( \partial / \partial x ^ {i} ) ( \partial / \partial x ^ {j} ) $.
2 KB (261 words) - 17:17, 5 June 2020
''of a first-order partial differential equation''
satisfying the equations
2 KB (337 words) - 16:43, 4 June 2020
...iaofmath.org/legacyimages/o/o070/o070660/o0706603.png" /> is the number of
equations and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.o
For example, an overdetermined system of linear algebraic
equations
5 KB (715 words) - 08:35, 19 October 2014
''in the theory of partial differential equations''
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...oundary value problem, elliptic equations|Boundary value problem, elliptic equations]]).
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...orms reduces (see [[Bonnet theorem|Bonnet theorem]]). The Peterson–Codazzi equations take the form
...rtial u^2}+\Gamma_{i1}^1b_{12}+\Gamma_{i1}^2b_{22}=\frac{\partial b_{i2}}{\partial u^1}+\Gamma_{i2}^1b_{11}+\Gamma_{i2}^2b_{21},$$
2 KB (308 words) - 14:42, 14 August 2014
...auchy problem|Cauchy problem]] for differential equations. For an ordinary differential equation in the form
For a partial differential equation, written in normal form with respect to a distinguished variable
2 KB (288 words) - 22:12, 5 June 2020
...artial differential equations|Boundary value problem, partial differential equations]]). Suppose, for example, that in a bounded domain $ \Omega $
\frac{\partial ^ {2} u ( x) }{\partial x _ {i} \partial x _ {j} }
2 KB (350 words) - 19:19, 11 September 2020
$#C+1 = 12 : ~/encyclopedia/old_files/data/P071/P.0701210 Parabolic partial differential equation
An equation (cf. [[Differential equation, partial|Differential equation, partial]]) of the form
2 KB (336 words) - 01:00, 24 December 2020
...unctions occurring in the differential equation (or system of differential equations) and all the initial data, together with the non-characteristic initial sur
partial differential equations in $ k $
7 KB (987 words) - 15:35, 4 June 2020