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《Chinese Annals of Mathematics,series A》 1981-01
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On a rectangular domain R(δ)={0≤t≤δ, 0≤x≤1}. (1) We consider the second initial-boundary value problem for the quasi-linear hyperbolicparabolic coupled systemWithout loss of generality, the initial conditions may be written as t=0: u_j=0,(j=1,…, n),v=0, and we can suppose thatThe boundary conditions are as follows: We assume that the following conditions are satisfied: (1)the orientabihty condition (2)the compatibility condition(3)the condition of characterizing number(4)The smoothness condition:the coefficients of the system and the boundary conditions are suitably smooth.By means of certain a priori estimations for the solution of the heat equation and the linear hyperbolic system, using an iteration method and Leray-Schauder fixed point theorem, we have provedTheorem 1. Under the preceding hypotheses, for the second initial-boundary value problem (2)—(4),(6),(7),there exists uniquely a classical solution on R(δ) where δ0 is suitably small.Theorem 2. In theorem 1, the condition of characterizing number(13) may be ameliorated as the following solvable condition: L.e., the boundary conditions(6),(7) may be written as
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Chinese Journal Full-text Database 1 Hits
1 YU Li-xin,GUO Yi-ming(Department of Mathematics and Informational Science,Yantai University, Yantai 264005,China);Local C~1 Solution to the Mixed Initial-boundary Value Problem for Quasilinear Hyperbolic Systems[J];Journal of Yantai University(Natural Science and Engineering Edition);2006-01
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