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The two-dimensional heat equation

Homog. Dirichlet BCsInhomog. Dirichlet BCsHomogenizingComplete solutionThe two-dimensional heat equationRyan C. DailedaTrinity UniversityPartial Differential EquationsLecture 12 DailedaThe 2-D heat equationHomog. Dirichlet BCsInhomog. Dirichlet BCsHomogenizingComplete solutionPhysical motivationGoal:Model heat flow in a two-dimensional object (thin plate).Set up:Represent the plate by a region in thexy-plane and letu(x,y,t) ={temperature of plate at position (x,y) a fixedt, the height of the surfacez=u(x,y,t) gives thetemperature of the plate at timetand position (x,y).}

one can show that u satis es the two dimensional heat equation u t = c2 u = c2(u xx + u yy) Daileda The 2-D heat equation. Homog. Dirichlet BCsInhomog. ... which is just the double Fourier series for f(x;y). Daileda The 2-D heat equation. Homog. Dirichlet BCsInhomog. ... If we know the sine series expansion for f 2(x) on [0;a], then we can use ...

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