By Boris Andreianov (auth.), Gui-Qiang G. Chen, Helge Holden, Kenneth H. Karlsen (eds.)
This ebook offers 13 papers, representing the main major advances and present tendencies in nonlinear hyperbolic conservation legislation and comparable research with purposes. themes lined comprise a survey on multidimensional structures of conservation legislation in addition to novel effects on liquid crystals, conservation legislation with discontinuous flux services, and purposes to sedimentation. additionally integrated are articles on fresh advances within the Euler equations and the Navier-Stokes-Fourier-Poisson method, as well as new effects on collective phenomena defined by way of the Cucker-Smale version.
The Workshop on Hyperbolic Conservation legislation and comparable research with purposes on the overseas Centre for Mathematical Sciences (Edinburgh, united kingdom) held in Edinburgh, September 2011, produced this advantageous number of unique study and survey articles. Many top mathematicians attended the development and submitted their contributions for this quantity. it really is addressed to researchers and graduate scholars attracted to partial differential equations and similar research with applications.
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Additional info for Hyperbolic Conservation Laws and Related Analysis with Applications: Edinburgh, September 2011
F. Otto, Initial-boundary value problem for a scalar conservation law. C. R. Acad. Sci. Paris S´er. I 322, 729–734 (1996) 27. Y. Panov, Existence of strong traces for generalized solutions of multidimensional scalar conservation laws. J. Hyperbolic Differ. Equ. 2(4), 885–908 (2005) 28. Y. Panov, Existence of strong traces for quasi-solutions of multidimensional conservation laws. J. Hyperbolic Differ. Equ. 4(4), 729–770 (2007) 29. G. Vallet, Dirichlet problem for a nonlinear conservation law. Rev.
We observe that Fig. 4 illustrates how the “overshoot” phenomenon diminishes as x ! 0. The numerical solutions of Examples 1 and 2 indicate that the STVD and FTVD schemes are significantly more accurate than their first-order counterpart. It seems that both schemes STVD and FTVD, have comparable accuracy. A significant difference in solution behaviour between both schemes becomes visible in Fig. 4. 4 A Note on Second-Order Degenerate Parabolic Equations (Example 3) The model (9) with a degenerate diffusion term can be handled by a Strangtype operator splitting scheme .
3. @x Ka …T Suitable Rankine-Hugoniot and entropy jump conditions can be derived from (41). The uniqueness of entropy solutions follows from a result proved in  regarding continuous dependence of entropy solutions with respect to the flux function: Theorem 2. If u and v are entropy solutions of (11) and (12) with initial data u0 and v0 , respectively, then for T > 0 there exists a constant C1 such that u. ; t/ v. R/ In particular, an entropy solution of (11) and (12) is unique. Finally, let us briefly address the convergence analysis and the related result of existence of entropy solutions.
Hyperbolic Conservation Laws and Related Analysis with Applications: Edinburgh, September 2011 by Boris Andreianov (auth.), Gui-Qiang G. Chen, Helge Holden, Kenneth H. Karlsen (eds.)