CAUCHY PROBLEM FOR NONLINEAR HYPERBOLIC SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS

[摘要] Consider the Cauchy problem for the system of nonlinear partial differential equations (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) where x(;; )(ELEM)(;; )(//R) x (//R)(;;N), D(;;m)u = {D(;;(alpha))u(VBAR) (VBAR)(alpha)(VBAR) = (VBAR)(alpha)(,0) + (.)(.)(.) + (alpha)(,N)(VBAR) (LESSTHEQ) m}, e(;; )=(;; )(e(,1), (.)(.)(.) , e(,n)), u = (u(,1), (.)(.)(.) , u(,n)), and suppose: (a) e(,k)(x,y)(;; )(ELEM)(;; )C(;;(INFIN))((//R) x (//R)(;;N) x (//R)(;;r) x (.)(.)(.) x (//R)(;;r)) n times where y(;; )=(;; )D(;;m)u, (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) (b) the matrix (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) is invertible for (alpha)(,0) = m, where y(,j(alpha)) = D(;;(alpha))u(,j), (c) the hyperbolicity condition is satisfied, i.e. (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)

[发布机构] Rice University