By S Kawashima, Taku Yanagisawa

Long ago twenty years, there was nice development within the concept of nonlinear partial differential equations. This e-book describes the development, concentrating on fascinating themes in fuel dynamics, fluid dynamics, elastodynamics and so forth. It includes ten articles, every one of which discusses a truly contemporary outcome acquired via the writer. a few of these articles evaluate comparable effects.

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M a t h . (1992), 273-304. Chen, Linear approximation of shock reflecton at a wedge with large angle, C o m m . P D E s (1996), 1103-1118. Chen, Linear approximation for supersonic flow past a delta wing ( to appear ) . Chen, On the stable method computing conical flow, M a t h . Numer. Sinica (1979), 377-384. 42 [ l l ] R . Friedrichs, supersonic flow and shock waves, Springer-Verlag, NewYork, 1948. Ebin, The initial boundayy value problem for subsoncc fluid motion, C o m m . P u r e Appl. 32 (1979), 1-19.

O) € R 2 and C / 0. 4) that the vector to satisfies the system in one space dimension: i a°{w)dtw + £ Qal(w)dsw = 0. 5) in the form tu(0,*) =£¥>(»). (1-6) where

2) and C${du) - 1, a°f(du) + c*6uSai) vanish at du = 0 at least of second order, that is, a°°(du) = \+0(\duf) = - c ? M a J + 0(|9u| 2 ) a°f(du) near du = 0. 00 We shall seek the eigenvalues A = A(tu) of the matrix a(w) and the corre­ sponding eigenvector £ = £(tu).

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