By Symposium on Nonlinear Evolution Equations University of Wisconsin-mad, Michael G. Crandall, Michael G. Crandall, University of Wisconsin--Madison Mathematics Research Center

ISBN-10: 0121952509

ISBN-13: 9780121952501

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Extra resources for Nonlinear Evolution Equations. Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, October 17–19, 1977

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P. Liu, Indiana Univ. Math. , 2^3, 147 (1977 ). f [13] T. P. Liu, A deterministic version of Glimm s method, [14] R. D. Richtmyer and K. W. Morton, Finite Difference to appear. Methods for Initial Value Problems, Interscience (1967). [15] G. Sod, to appear. [16] B. Wendroff, J. of Math. 3_8 , 454 (1972). [17] F. A. Williams, Combustion theory, Addison Wesley (1965). Partially supported by US ERDA at the Lawrence Berkeley Laboratory. Department of Mathematics University of California Berkeley, California 94720 27 Nonlinear Evolution Equations The Initial Value Problem of the Boltzmann Equation and Its Fluid Dynamical Limit at the Level of Compressible Euler Equation Takaaki 1.

1. Non homogeneous Bingham's fluids. 2. The problem when p°> 0. 3. The case ji = 0. 4. Other models. 5. Unilateral problems and estimates on frac­ tional t-derivatives. Asymptotic expansions of solutions in flows in media with periodic obstacles. 1. Setting of the problem. 2. Formal structure of the expansion. 3. Analytic computations. 4. Boundary conditions on p Q, p 1# ... 5. Summary of formulas. Bibliography. ^ Similar questions for non newtonian fluids will be consid­ ered in latter papers.

14. J. McLennan (19 65), Convergence of the Chapman-Enskog expansion for the linearized Boltzmann equation, Phys. of Fluids, 8, 1580-1584. 15. B. Nicolaenko and J. Thurber (1975), Weak shock and bifurcating solutions of the nonlinear Boltzmann equation, J. de Mecanique, L4, 305-338. 16. B. Nicolaenko (1974), Shock wave solutions of the Boltzmann equation as a nonlinear bifurcation problem from the essential spectrum. Coll. Intern. CNRS n° 236, Theories Cinetiques Classiques et Relativistes, 127-150, Paris.

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Nonlinear Evolution Equations. Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, October 17–19, 1977 by Symposium on Nonlinear Evolution Equations University of Wisconsin-mad, Michael G. Crandall, Michael G. Crandall, University of Wisconsin--Madison Mathematics Research Center


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