Well-Posedness Theory for a Nonconservative Burgers-Type System Arising in Dislocation Dynamics
In this work we study a system of nonconservative Burgers type in one space dimension, arising in modeling the dynamics of dislocation densities in crystals. Starting from physically relevant initial data that are of a special form, namely nondecreasing, periodic plus linear functions, we prove the...
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| Veröffentlicht in: | SIAM journal on mathematical analysis 2007-01, Vol.39 (3), p.965-986 |
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| creator | El Hajj, Ahmad |
| description | In this work we study a system of nonconservative Burgers type in one space dimension, arising in modeling the dynamics of dislocation densities in crystals. Starting from physically relevant initial data that are of a special form, namely nondecreasing, periodic plus linear functions, we prove the global existence and uniqueness of a solution in $H^1_{loc}(\mathbb R\times[0,+\infty))$ that preserves the nature of the initial data. The approach is made by adding some viscosity to the system, obtaining energy estimates, and passing to the limit for vanishing viscosity. A comparison principle is shown for this system as well as an application in the case of the classical Burgers equation. |
| doi_str_mv | 10.1137/060672170 |
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| ispartof | SIAM journal on mathematical analysis, 2007-01, Vol.39 (3), p.965-986 |
| issn | 0036-1410 1095-7154 |
| language | eng |
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| source | LOCUS - SIAM's Online Journal Archive |
| subjects | Applied mathematics Eigenvalues Estimates Mathematics Viscosity |
| title | Well-Posedness Theory for a Nonconservative Burgers-Type System Arising in Dislocation Dynamics |
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