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《Chinese Annals of Mathematics,series A》 1981-01
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SECOND INITIAL-BOUNDARY VALUE PROBLEMS FOR QUASI-LINEAR HYPERBOLIC-PARABOLIC COUPLED SYSTEMS

LI DAQIAN(LEE DA-TSIN) Yu WENCHI(Yu WEN-TZU) SHEN WEIXI(SHEN WE-SHI) (Fudan University)  
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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【References】
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
【Citations】
Chinese Journal Full-text Database 1 Hits
1 Li Da-qian(Li Ta-tsien);Yu Wen-ci(Yu Wen-tzu);Shen Wei-xi Fudan University;CAUCHY'S PROBLEM FOR QUASILINEAR HYPERBOLIC-PARABOLIC COUPLED SYSTEMS[J];Acta Mathematicae Applicatae Sinica;1981-04
【Co-citations】
Chinese Journal Full-text Database 4 Hits
1 JIA Wen?xin 1,SHA Meng?lin 2 (1.Dept. of Basic Courses, North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450045, China; 2.President Office, Shanghai Tiedao Univ., Shanghai 200331, China)[WT5HZ];Effect of Relaxation for Motion Systems in Positive Compress Gas Dynamics[J];JOURNAL OF SHANGHAI TIEDAO UNIVERSITY(NATURAL SCIENCE EDITION);2000-02
2 Liu Fagui (Inst. of Math., FudanUniv., Shanghai, 200433);Effects of Relaxation for A Class of Quasilinear Hyperbolic Conservation Laws[J];JOURNAL OF MATHEMATICAL STUDY;1997-01
3 Guo Dali(Department of Basic Courses);GLOBAL SMOOTH SOLUTION OF THERMALLY INSULATED GAS DYNAMICS EQUATIONS[J];Journal of Southwest Petroleum Institute;1993-01
4 LI CAIZHONG(Institute of Mathematics, Shantou University, Shantou 266003 Department of Mathematics, Sichuan United University, Chengdu 610065)LIU FAGUI(Department of Basic Courses, North China Institute of Water Conser. & Hydro. Power, Zhengzhou 450045);P-SYSTEMS WITH RELAXATION[J];ACTA MATHEMATICAE APPLICATAE SINICA;1997-01
【Co-references】
Chinese Journal Full-text Database 2 Hits
1 YU Lixin Institute of Mathematics, Fudan University, Shanghai 200433, China.;SEMI-GLOBAL C1 SOLUTION TO THE MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR A KIND OF QUASILINEAR HYPERBOLIC SYSTEMS[J];Chinese Annals of Mathematics,series A;2004-05
2 Zhiqiang WANG School of Mathematical Sciences, Fudan University, Shanghai 200433, China.;Exact Controllability for Nonautonomous First Order Quasilinear Hyperbolic Systems[J];数学年刊B辑(英文版);2006-06
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