The Florin problem for a quasilinear parabolic equation (Q2742838)
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scientific article; zbMATH DE number 1650912
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Florin problem for a quasilinear parabolic equation |
scientific article; zbMATH DE number 1650912 |
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24 September 2001
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quasilinear parabolic equation
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Schauder type a priori estimates
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existence
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uniqueness
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0.9424881
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0.88405675
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0.88151944
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0.87730455
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0.87351304
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0.87109864
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0.8665165
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The Florin problem for a quasilinear parabolic equation (English)
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The authors consider the free boundary problem for the quasilinear parabolic equation [see \textit{A. Fasano} and \textit{M. Primicerio}, J. Math. Anal. Appl. 72, 247-273 (1979; Zbl 0421.35080)] NEWLINE\[NEWLINEu_t=a(t,x,u_x)u_{xx} +b(t,x,u_x)NEWLINE\]NEWLINE in \(D=\{(t,x)\mid 0<t\leq T, 0<x<s(t)\}\) with nonlocal boundary conditions \(u(0,x)=\varphi(x), x\in[0,s_0]; u_x(t,0)=\psi_1(t), t\in[0,T]; u_x(t,s(t))= \psi_2(t), t\in[0,T]; \alpha u(t,0)=u(t,s(t)), t\in[0,T]\), where \(s_0=s(0)>0\) is considered. Existence and uniqueness theorems are proved on the base of Schauder type a priori estimates.
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