二阶复合型偏微分方程的函数论方法

FUNCTION THEORETIC METHODS FOR THE COMPOSITE SYSTEMS OF SECOND ORDER DIFFERENTIAL EQUATIONS

本文讨论二阶复合型方程组（ＣＥ２）：１００１２ｔ２＋１００λ／Ｒ２２ｘ２１＋０（λ－ｋ２）／ｋ２（λ－１）／ｋ０２ｘ１ｘ２＋λ００１２ｘ２２ｕ１ｕ２＝０（０＜ｋ＜１，λ＜０）得到了该方程组有解的必要条件，并由此知道该方程组的Ｃａｕｃｈｙ问题是不适定的，转而讨论问题（Ｄ２），证明了问题（Ｄ２）是可解的。

In this paper,we consider the second order composite system (CE2):10012t2+100λ/k22x21+0(λ-k2/k2)(λ-1)/k02x1x2+λ0012x22u1u2=0 (0<k<1,λ<0)and obtain the necessary condition of the solvability for system (CE2),and know that the cauchy problem for system (CE2) is not correct posed.So we turn to consider the problem (D2).and prove the solvability of this problem and give the representation of the solution.