Question

Adjoint operator of heat partial differential equation

Answer 1

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In this example, the heat equation in two dimensions predicts that if one area of an otherwise cool metal plate has been heated, say with a torch, over time the temperature of that area will gradually decrease, starting at the edge and moving inward. Meanwhile, the part of the plate outside that region will be getting warmer. Eventually the entire plate will reach a uniform intermediate temperature. In this animation, both height and color are used to show temperature.