Quasilinearization for some nonlocal problems (Q2367431)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quasilinearization for some nonlocal problems |
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Quasilinearization for some nonlocal problems (English)
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11 August 1993
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Summary: The method of generalized quasilinearization is applied to study semilinear parabolic equations \(u_ t-Lu = f(t,x,u)\) with nonlocal boundary conditions \(u(t,x) = \int_ \Omega \varphi (x,y) u(t,y)dy\). The convexity of \(f\) in \(u\) is relaxed by requiring \(f(t,x,u) + Mu^ 2\) to be convex for some \(M>0\). The quadratic convergence of monotone sequences is obtained.
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upper and lower solutions
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monotone iterative technique
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generalized quasilinearization
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semilinear parabolic equations
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nonlocal boundary conditions
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quadratic convergence
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