Adimurthi, . ; Singh, Manish ; Veerappa Gowda, G.D. (2020) Lax-Oleĭnik explicit formula and structure theory for balance laws Journal of Differential Equations, 268 (11). pp. 6517-6575. ISSN 0022-0396
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Official URL: http://doi.org/10.1016/j.jde.2019.11.044
Related URL: http://dx.doi.org/10.1016/j.jde.2019.11.044
Abstract
In this paper, we study the structure of solutions for the Balance Laws in one space dimension with a source term having the form {u t+ f (u) x− α (t) u= 0 in R×(0,∞) u (x, 0)= u 0 on R×{t= 0}. Consequently, we show that the behaviour of the shock packets and the phenomenon of one shock situation is completely different when compared to equations without a source term. Moreover, contrary to the behaviour of shock packets in conservation laws, in our situation, we show that the slope of the left boundary of the shock packet can be strictly greater than that of the right boundary.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| Keywords: | Balance Laws; Riemann Problem; Hamilton-Jacobi Equation; Structure Theorem; Asymptotically Single Shock Packet; Lax-Oleĭnik Formula. |
| ID Code: | 119763 |
| Deposited On: | 17 Jun 2021 04:39 |
| Last Modified: | 17 Jun 2021 04:39 |
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