Difference between revisions of "Linear boundary value problem"
From Encyclopedia of Mathematics
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| − | + | The problem of determining in a domain $D$ of the variable $x = (x_1,\ldots,x_n)$ the solution $u(x)$ of a linear differential equation | |
| − | + | $$ | |
| − | which satisfies on the boundary | + | (Lu)(x) = f(x), \quad x\in D, |
| − | + | $$ | |
| − | + | which satisfies on the boundary $S$ of this domain (or on a part of it) the linear boundary conditions | |
| − | + | $$ | |
| − | See also [[ | + | (Bu)(y) = \phi(y), \quad y\in S. |
| + | $$ | ||
| + | See also [[Boundary value problem, ordinary differential equations]]; [[Boundary value problem, partial differential equations]]. | ||
Latest revision as of 21:19, 2 May 2012
2020 Mathematics Subject Classification: Primary: 34B05 [MSN][ZBL]
The problem of determining in a domain $D$ of the variable $x = (x_1,\ldots,x_n)$ the solution $u(x)$ of a linear differential equation $$ (Lu)(x) = f(x), \quad x\in D, $$ which satisfies on the boundary $S$ of this domain (or on a part of it) the linear boundary conditions $$ (Bu)(y) = \phi(y), \quad y\in S. $$ See also Boundary value problem, ordinary differential equations; Boundary value problem, partial differential equations.
How to Cite This Entry:
Linear boundary value problem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Linear_boundary_value_problem&oldid=25857
Linear boundary value problem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Linear_boundary_value_problem&oldid=25857
This article was adapted from an original article by A.P. Soldatov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article