Show that the backward heat equation u t = k 2u x2 , subject to u(0, t) = u(L, t) = 0
Chapter 2, Problem 2.4.21(choose chapter or problem)
Show that the backward heat equation u t = k 2u x2 , subject to u(0, t) = u(L, t) = 0 and u(x, 0) = f(x), is not well posed. [Hint: Show that if the data are changed an arbitrarily small amount, for example, f(x) f(x) + 1 n sin nx L for large n, then the solution u(x, t) changes by a large amount.]
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