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Partial Differential Equations - uni-leipzig.de

Partial Differential EquationsLecture NotesErich MiersemannDepartment of MathematicsLeipzig UniversityVersion October, 20122 Contents1 Examples .. Equations from variational problems .. Ordinary differential Equations .. Partial differential Equations .. Exercises .. 222 Equations of first Linear Equations .. Quasilinear Equations .. A linearization method .. Initial value problem of Cauchy .. Nonlinear Equations in two variables .. Initial value problem of Cauchy .. Nonlinear Equations inRn.

1.1. EXAMPLES 11 y y 0 x x y 1 0 1 x Figure 1.2: Boundary value problem the unknown function u(x,y) is for example F(x,y,u,ux,uy,uxx,uxy,uyy) = 0, where the function F is given.

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