... **ENTROPY** **SOLUTIONS** OF MULTIDIMENSIONAL SCALAR CONSERVATION LAWS GUI-QIANG CHEN ST ´ EPHANE JUNCA MICHEL RASCLE ...for **entropy** so- lutions only in L ∞ of multidimensional scalar conservation laws is ...

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... (strong) **solutions** with classical derivatives can not ...time) **solutions**, weak **solutions** must be defined, where the derivatives are defined in the sense of ...Weak **solutions** do exist globally ...

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... Abstract In this article, we investigate the BV stability of 2×2 hyperbolic systems of conserva- tion laws with strictly positive velocities under dissipative boundary conditions. More precisely, we derive sufficient ...

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... of **entropy** **solutions** [ 23 , 42 , 43 ...the **entropy** **solutions** of ( 1 ) in BV s , with BV s data has been done in [ 13 ] and with L ∞ data in the same spaces in [ 13 , 38 , 39 ...that ...

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... measure **solutions** for ...measure **solutions** was shown in [ 24 ...bounded **entropy** **solutions** are provided with an optimal fractional BV regularity for the initial data u 0 ...

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... **entropy** **solutions**. To be more precise, in this paper, we will consider **solutions** ` a la Glimm [15], that is, **entropy** **solutions** in the sense above, of small total variation in x for all ...

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... s . We extend the smoothing eect proved in [BGJ] for any C 1 strictly convex ux, more general than a ux with a power law behavior. The rst tool which has provided optimal regularity results is the Lax-Olenik ...

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... kinetic **solutions**), nor the fine regularization estimates of the super-critical case [ 43 ...2 **entropy** **solutions**, and give the uniqueness result based upon the automatic boundary regularity of such ...

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... imum principle: ess inf u 0 ≤ u ≤ ess sup u 0 . If α ∈ (1, 2], all **solutions** to (2.7)–(2.8) with bounded initial conditions are smooth and global-in-time (see [8, 16, 17]). On the other hand, the occurrence of ...

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... these **solutions** satisfy the Clausius inequality: the change of the free energy is bounded by the work done by the boundary ...thermodynamic **solutions**, and we conjecture their ...weak **solutions**, ...

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... −c j | is convergent. § 5. Godunov scheme There is two diﬀerent approaches to build a Godunov scheme for the system (1.12)-(1.13): the first one uses the “natural” space-time framework (the evolution variable is t), the ...

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... Accordingly to Lemma 2 in [23], there exists a family of half-plain supported **entropy**-**entropy** fluxes (η, q) such that η and q are bounded together with their first and second derivatives. These are ...

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... of **entropy** **solutions** The Lipschitz continuous dependence of **entropy** **solutions** with respect to initial data can be derived using Kruˇ zkov’s doubling of variable technique [13] as in [3, 4, ...

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... 1.5. Our second problem: ruling out pathologies in timed automata An amazing theoretical application of the **entropy** of timed languages is related to a well-known, but not yet sufficiently understood issue of ...

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... of VMs that need to migrate as compared to the amount of available resources only exacerbates these problems. Thus, it is essential that consolidation be as efficient and reactive as possible. In this paper, we propose ...

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... the maximal number of points than can be included in a set ∆ that has **entropy** smaller than B. In other words, it is the maximal number of points in Υ m or Υ m that can be collected by a path of **entropy** ...

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... tanglement **entropy** is given by S EE = lim n→1 S RE (n) = − lim n→1 ∂n ∂ tr A (ρ A ) n ...entanglement **entropy** with the area of an extremal surface in an anti- de Sitter space, while Maldacena and Susskind ...

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... maximum **entropy** production (MEP) that al- lowed (Paltridge, 1975) to derive the distribution of heat and clouds at the Earth surface with reasonable accuracy, with- out any parameters and with a model of a dozen ...

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... in other compact metric spaces that are not manifolds? For instance, do they hold if the space is a Cantor set K? If the aim were just to construct f ∈ Hom(K) with ergodic mea- sures with infinite metric **entropy**, ...

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... The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au[r] ...

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