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

Sample text

For n=0,l,2,••• . Therefore if we suppose 0 < E < e /4 and set 2 a = 1 - /1-4 C ( W * N 1C 2E / e ) 1, we get 2 S3 C d / < - > L L L M . , < - f 2 N ( . ) | | L a n ) M£ * (a | | | f < » > ( . 15) and decays to zero in B 00 as t . 3. £ > 2. 15) with e fixed exists in the space B^ ^ uniquely 00 in the large in time and decays to zero as t -* . 1. 3. 1) converges to the 00 absolute Maxwellian distribution as t •> , provided that the initial deviation from it is small in the norm of B (m>3, 0 m, Jo £>2) .

18. (1976), A general class of nonlinear bifurcation problems from a point in the essential spectrum ; Appl. to shock wave solutions of kinetic equations, Symp. on Appl. of Bifurcation Theory, Univ. of Wisconsin-Madison. L. Nirenberg (1972) , An abstract form of the nonlinear Cauchy-Kowalewski theorem, J. Diff. Geometry, 6, 561-576. Initial Value Problem of the Boltzmann Equation 19. T. Nishida and K. Imai (1976), Global solutions to the initial value problem for the nonlinear Boltzmann equation, Publ.

9). The uniform continuity in t is given by the following. 3. 2. 27)|||f e(t)-f e(s)||| m_ a f_ j apl f _< C 2E{ for 0 < s < t and for a fixed o e (0,1/2) , where C 2 is independent of e e (0,1]. 11). See Nishida (preprint). We only remark that the Q Holder-coefficient has the singularity of l/t as t 0, which corresponds to the initial layer of the rarefied gas motion described by Boltzmann equation. 28) f E(t) - f 0(t) in B _ m 0 _ta pti, The limit function has the bound 0

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