Adimurthi, . ; Ghoshal, Shyam Sundar ; Gowda, G. D. Veerappa (2012) Structure of entropy solutions to scalar conservation laws with strictly convex flux Journal of Hyperbolic Differential Equations, 09 (04). pp. 571-611. ISSN 0219-8916
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Official URL: http://www.worldscientific.com/doi/abs/10.1142/S02...
Related URL: http://dx.doi.org/10.1142/S0219891612500191
Abstract
We consider scalar conservation laws in one space dimension with convex flux and we establish a new structure theorem for entropy solutions by identifying certain shock regions of interest, each of them representing a single shock wave at infinity. Using this theorem, we construct a smooth initial data with compact support for which the solution exhibits infinitely many shock waves asymptotically in time. Our proof relies on Lax–Oleinik explicit formula and the notion of generalized characteristics introduced by Dafermos.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to World Scientific Publishing Company. |
| Keywords: | Hamilton–Jacobi Equation; Scalar Conservation Laws; Characteristic Lines; Asymptotically Single Shock Packet |
| ID Code: | 112166 |
| Deposited On: | 31 Jan 2018 04:31 |
| Last Modified: | 31 Jan 2018 04:31 |
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