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On a Hamilton-Jacobi equation. (English) Zbl 0704.35029

Author’s summary: “We prove a theorem of existence and uniqueness for the problem: \[ \frac{\partial}{\partial u}\phi \frac{\partial}{\partial v}\phi +\sum a_{jk}(u,v,z)\frac{\partial}{\partial z_ j}\phi \frac{\partial}{\partial z_ k}\phi =0 \] with data: \(\phi (u,v,z,\eta)=z\cdot \eta\) for \(uv=0\), on a strip [0,U]\(\times {\bar {\mathbb{R}}}^+\times {\mathbb{R}}^ n\times {\dot {\mathbb{R}}}^ n\) where \(A=(a_{jk})\) is a \(C^{\infty}\), \(n\times n\), negative definite real matrix.
Reviewer: J.Wloka

MSC:

35F20 Nonlinear first-order PDEs
70H20 Hamilton-Jacobi equations in mechanics
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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References:

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