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- W2078256973 abstract "Let a, b, c, d, f, g be analytic functions of two real variables $x,y$ in the $z = x + yi$ plane. Consider the elliptic system: [frac{{partial u}} {{partial x}} - frac{{partial v}} {{partial y}} = au + bv + f,qquad frac{{partial v}} {{partial x}} + frac{{partial u}} {{partial y}} = cu + dy + g.] The following topics connected with the Cauchy problem of the abovementioned system will be investigated: (i) The necessary and sufficient conditions for the existence of the global solutions. (ii) The estimate of the “stability” of the solutions. (iii) The method for constructing the global solution. (iv) The construction of the approximate solution with the imprecise data. (v) The generalizations to the quasi-linear analytic elliptic system: [frac{{partial u}}{{partial x}} - frac{{partial v}}{{partial y}} = f_1 (u,v,x,y) qquad {text{and}}qquad frac{{partial v}}{{partial x}} + frac{{partial u}}{{partial y}} = f_2 (u,v,x,y).]" @default.
- W2078256973 created "2016-06-24" @default.
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- W2078256973 date "1977-08-01" @default.
- W2078256973 modified "2023-10-16" @default.
- W2078256973 title "Cauchy’s Problem for Systems of First Order Analytic Elliptic Equations in the Plan" @default.
- W2078256973 doi "https://doi.org/10.1137/0508056" @default.
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