On the existence of global solutions of the Cauchy problem for Hamilton-Jacobi equations (Q1915892)
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scientific article; zbMATH DE number 894956
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the existence of global solutions of the Cauchy problem for Hamilton-Jacobi equations |
scientific article; zbMATH DE number 894956 |
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On the existence of global solutions of the Cauchy problem for Hamilton-Jacobi equations (English)
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3 March 1997
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The paper is concerned with the existence of global quasi-classical solutions to the problem \[ u_t + H(t, \nabla_x u) = 0, \quad u(0,x) = u_0 (x), \quad x \in R^n. \] Several existence results are provided with the help of a modified Hopf formula, including the existence of Lipschitz solutions. Illustrative examples are also provided.
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Cauchy problem
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Hamilton-Jacobi equation
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Hopf formula
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Lipschitz solutions
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0.8821765780448914
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0.8693332672119141
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