The two dimensional heat equation - Trinity University

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The 2D heat equation Homogeneous Dirichlet boundary conditions Steady state solutionsSteady state solutionsTo deal with inhomogeneous boundary conditions in heatproblems, one must study the solutions of the heat equationthat do not vary with time.These are the steady state solutions. They satisfyu t = 0.In the 1D case, the heat equation for steady states becomesu xx = 0.The solutions are simply straight lines.DailedaThe 2D heat equation
The 2D heat equation Homogeneous Dirichlet boundary conditions Steady state solutionsLaplace’s equationIn the 2D case, we see that steady states must solve∇ 2 u = u xx +u yy = 0. (7)This is Laplace’s equation.Solutions to Laplace’s equation are called harmonicfunctions.See assignment 1 for examples of harmonic functions.DailedaThe 2D heat equation
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The two dimensional heat equation - Trinity University

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