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- W2391226367 abstract "In this paper we study the relation between symmetric positivo systems and equations of higher order. The main result is:Theorem 1. An equation of second order LΦ=f can be transfromed into a symmetric positive system by introducing new unknown functionsu_i=sum from j=0 to n (a_(ij)φ_j(i=0, 1, …, n)), φ_0=φ, φ_j=((?)φ)/((?)x_j) iff there exists L_1 of order 1 such thatRe(L_1φ·(?)=sum from i=1 to n ((?)P_i(φ, φ)+B(φ, φ)), where P_i(φ, φ)(i=1, …, n), B(φ, φ)are differential quadartic froms and B(φ, φ) is positive definite.This Theorem can be extended into equations of higher order.Some examples of deducing equations of higher order into symmetric positive systems are given.Finally, we give a counter example which shows that a boundary problem of a symmetric positive system deduced from an equation of higher order is admissible, but its corresponding bounbary problem of the original equation is not well-posed." @default.
- W2391226367 created "2016-06-24" @default.
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- W2391226367 date "1982-01-01" @default.
- W2391226367 modified "2023-09-25" @default.
- W2391226367 title "PARTIAL DIFFERENTIAL EQUATIONS OF HIGHER ORDER AND SYMMETRIC POSITIVE SYSTEMS" @default.
- W2391226367 hasPublicationYear "1982" @default.
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