...= 35 : ~/encyclopedia/old_files/data/D031/D.0301960 Differential equation, partial, discontinuous initial (boundary) conditions
A problem involving partial differential equations in which the functions specifying the initial (boundary) conditions are not
7 KB (984 words) - 17:33, 5 June 2020
A partial differential equation of the form
\frac{\partial ^ {2} u }{\partial t ^ {2} }
6 KB (798 words) - 05:40, 19 March 2022
$#C+1 = 19 : ~/encyclopedia/old_files/data/H046/H.0406200 Hamilton equations
Ordinary canonical first-order differential equations describing the motion of holonomic mechanical systems acted upon by externa
3 KB (478 words) - 19:43, 5 June 2020
''of a differential equation
...[[Strong solution|Strong solution]])? For example, in the case of elliptic equations, every weak solution is strong.
2 KB (280 words) - 08:28, 6 June 2020
$#C+1 = 140 : ~/encyclopedia/old_files/data/A012/A.0102940 Approximation of a differential operator by difference operators
An approximation of the differential operator by parameter-dependent operators such that the result of their app
11 KB (1,674 words) - 14:30, 7 April 2020
...riables (cf. [[Hyperbolic partial differential equation|Hyperbolic partial differential equation]]),
\frac \partial {\partial x }
6 KB (932 words) - 08:11, 6 June 2020
...utonomous system|autonomous system]] of second-order ordinary differential equations
...inary differential equations|Sector in the theory of ordinary differential equations]]) by semi-trajectories (the separatrices of the saddle node) approaching
4 KB (577 words) - 09:06, 1 October 2023
The differential expression
\frac{\partial F }{\partial p _ {k} }
3 KB (480 words) - 22:14, 5 June 2020
...u , \frac { \partial u } { \partial x _ { 1 } } , \frac { \partial u } { \partial x _ { 2 } } \right\} \end{equation*}
...{ \partial x _ { 1 } ^ { \prime } } , \frac { \partial u ^ { \prime } } { \partial x _ { 2 } ^ { \prime } } \right\} \end{equation*}
8 KB (1,072 words) - 17:02, 1 July 2020
for a hyperbolic partial differential equation
\frac{\partial ^ {2} u }{\partial t ^ {2} }
4 KB (558 words) - 07:57, 16 April 2023
''in the theory of differential equations''
...ssumption that an auxiliary equation or inequality (system of differential equations or inequalities) possesses a certain property.
8 KB (1,142 words) - 17:45, 4 June 2020
\frac{\partial X ^ {j} }{\partial x ^ {i} }
...n="top"> K.P. Rybakovskii, "The homotopy index and partial differential equations" , Springer (1987) (Translated from Russian)</TD></TR></table>
2 KB (300 words) - 08:21, 21 March 2022
...ia/old_files/data/P075/P.0705400 Prolongation of solutions of differential equations
The property of solutions of ordinary differential equations to be extendible to a larger interval of the independent variable. Let
6 KB (936 words) - 08:08, 6 June 2020
...ion has the Painlevé property (cf. [[Painlevé-type equations|Painlevé-type equations]]). If the equation cannot be transformed to one of those on the list, then
Generalized cylindrical Korteweg–de Vries equations (KdV, cf. [[Korteweg–de Vries equation|Korteweg–de Vries equation]]) ar
6 KB (840 words) - 11:54, 25 January 2022
...125 : ~/encyclopedia/old_files/data/D031/D.0301920 Differential equation, partial
\frac{\partial ^ {k} u }{
21 KB (2,842 words) - 02:26, 23 January 2022
$#C+1 = 42 : ~/encyclopedia/old_files/data/H048/H.0408300 Hyperbolic partial differential equation
A partial differential equation for which the [[Cauchy problem|Cauchy problem]] is uniquely solvab
6 KB (850 words) - 22:11, 5 June 2020
...ystem]]); these conditions are assumed to be expressible as non-integrable differential relations
The constraints (1) are said to be stationary if $ \partial \phi / \partial t \equiv 0 $.
4 KB (611 words) - 08:03, 6 June 2020
...oblem|Stefan problem]]). For example, find the flow $q(t)=\partial u(0,t)/\partial x$ from the conditions:
$$\frac{\partial u}{\partial t}=a^2\frac{\partial^2u}{\partial x^2},\quad0<x<\xi(t),\quad0<t\leq T,$$
2 KB (266 words) - 10:51, 10 August 2014
...iffusion equation]]) modelling the electrical activity of nerve cells. The equations have the form
$$\frac{\partial V}{\partial t}=\delta\frac{\partial^2V}{\partial x^2}+I+F(V,y_1,y_2,y_3),$$
2 KB (295 words) - 12:01, 26 July 2014
$#C+1 = 49 : ~/encyclopedia/old_files/data/A012/A.0102790 Appell equations
...oposed by J.W. Gibbs [[#References|[3]]] for holonomic systems. The Appell equations in independent Lagrange coordinates $ q _ {s} $(
4 KB (661 words) - 14:38, 10 March 2024