Nonlinear singular integral equations on a finite interval (Q2767545)
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scientific article; zbMATH DE number 1697674
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonlinear singular integral equations on a finite interval |
scientific article; zbMATH DE number 1697674 |
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23 January 2003
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nonlinear singular integral equation
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Riemann-Hilbert-type boundary value problem
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boundary seepage problem
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Nonlinear singular integral equations on a finite interval (English)
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The nonlinear singular integral equation NEWLINE\[NEWLINEu(x)= \int^1_{-1} {F\bigl(y, u(y)\bigr) \over y-x} dy+f(x),- 1\leq x\leq 1NEWLINE\]NEWLINE is studied. The equation is reduced to a Riemann-Hilbert-type boundary value problem for holomorphic functions in the complex unit disk. Conditions for the existence of solutions of the equation are given.NEWLINENEWLINENEWLINEAs an example a free boundary seepage problem from a channel is considered.
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