Transcription of Partial Differential Equations - uni-leipzig.de
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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.. Hamilton-Jacobi theory .. Exercises.
equation ut = k4u, where 4u = ux1x1 +ux2x2 +ux3x3 and k is a positive constant. The condition u(x,0) = u0 where u0(x) is given, is an initial condition associated to the above heat equation. The condition where h(x,t) is given is a boundary condition for the heat equation. If h(x,t) = g(x), that is, h is independent of t, then one expects that the
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