数学学报 1959, 9(4) 365-381 DOI:   cnki:ISSN:0583-1431.0.1959-04-000   ISSN: 0583-1431 CN: 11-2038/O1

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董光昌
查甫雷金方程的唯一性定理(Ⅲ)
董光昌
浙江大学
摘要: <正> 考虑下列混合型方程的唯一性问题K(y)u_(xx)+u_(yy)=0(K(0)=0;当y≠0时,dK/dy>0).(1)所考虑的区域由三条曲线围成.其一是双曲区域中由原点引出的特征线Г_1,它满足下面方程
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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 [1] and [2].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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收稿日期 1956-11-09 修回日期 1900-01-01 网络版发布日期  
DOI: cnki:ISSN:0583-1431.0.1959-04-000
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