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DEM0NSTRAT10 MATHEMATICAVol. XXVINo 3-41993J. Wolska-BochenekGENERALIZED INITIAL VALUE PROBLEMFOR FOURTH ORDER EQUATION OF ELLIPTIC T Y P EDedicated to the memory of Professor W1T0LDPOGORZELSKI1. IntroductionInitial value problems for elliptic partial differential equations occur inmany problems of mathematical physics for instance in geology, elasticity,aerodynamics. Problems of such a type were studied by many authors,among others A. K. Aziz and R. P. Gilbert [1], [2], D. L. Colton [3], [4]for the second order elliptic equations in two independent variables. In [5]D. L. Colton was studying the Cauchy problem for a class of fourth-order elliptic equations. J. Conlan and R. P. Gilbert were investigating the equationof the type [6](1)AAu = / ( x , y, u, ux, uy, uxx, uyy, Aux,Auy)where / was analytic, and subject to the following initial conditions(2)a[k^Aux + a^Auy+ a[k^uxx + a(k)uyy+ a^uxy+a[k\x+aj k ^u y + agfc^tt + a =0.In conditions (2) a\k^ =for k = 1,3, i = 1 , . . . , 9 on y = fk(x),kand= a\ \y) for k = 2,4, i = 1 , . . . , 9 on x = fk(y), the data beinganalytic.R. P. Gilbert and Wei Lin [7] were studying the equation(3)AAu + auxx - 2buxy + cuyy
Demonstratio Mathematica – de Gruyter
Published: Jul 1, 1993
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