Adimurthi, . ; Gowda, G. D. Veerappa (2010) Neumann boundary condition for a non-autonomous Hamilton-Jacobi equation in a quarter plane Indian Journal of Pure and Applied Mathematics, 41 (1). pp. 199-224. ISSN 0019-5588
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Official URL: http://doi.org/10.1007/s13226-010-0001-5
Related URL: http://dx.doi.org/10.1007/s13226-010-0001-5
Abstract
We consider Hamilton-Jacobi equation u t +H(u, u x ) = 0 in the quarter plane and study initial boundary value problems with Neumann boundary condition on the line x = 0. We assume that p → H(u, p) is convex, positively homogeneous of degree one. In general, this problem need not admit a continuous viscosity solution when s → H(s, p) is non increasing. In this paper, explicit formula for a viscosity solution of the initial boundary value problem is given for the cases s → H(s, p) is non decreasing as well as s → H(s, p) is non increasing.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Indian National Science Academy. |
| ID Code: | 119774 |
| Deposited On: | 17 Jun 2021 05:22 |
| Last Modified: | 17 Jun 2021 05:22 |
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