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MSC2000 唯一性定理:9845,充分条件:992,唯一性问题:809,数学学报:654,混合型方程:476,椭圆区域:466,存在性:411,能量
UNIQUENESS THEOREM FOR CHAPLYGIN'S PROBLEM(Ⅲ)
TONG KWANG-CRANG(Chekiang University)
Abstract: In this paper the uniqueness problem of the Cha-for y≠0)is considered.The domain D is bounded(?)by three curves showing in the figure,where T_1 and T_2are characteristics defined by the equation dx~2+Kdy~2=O,T_3 is a continuous curve.Let the coordinate of P be(Xo/yo)and the minimum and maximum abscissas ofT_3 be x_1 and x_2.When y<0,let 1+2(K/k_y)=f(y)and(?)Let in(n=0,1,2)be the least positive roots of the following equations:(?)Where δ=0 or 1 according to x_0+2Y(?) Finally,let y_1=0 if f(y)>0 for all y0≤y<0,otherwise let y1 be the upperbound of values y in the interval yo≤y<0 satisfying f(y)<0.Theorem.If y1<0 and there exists a positive numberεand an integer n(n=0,1,2)such that the following relation holds for yo≤y≤y1:(?)and if u is a quasi-regular solution which vanishes on T_2+T_3,then u=0 in D.The example for gas dynamical problem shows that this theorem is better than theresult of  and .The method of proof of the theorem is to consider the sum of the energy integral(?)dxdy=0 and the zero integral(?)(Pu~2)+
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DOI: cnki:ISSN:0583-1431.0.1959-04-000

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