A thin wire coinciding with the x-axis on the interval [ -L, L] is bent into the shape

Chapter 13, Problem 7

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A thin wire coinciding with the x-axis on the interval [ -L, L] is bent into the shape of a circle so that the ends x = -L and x = L are joined. Under certain conditions the temperature u(x, t) in the wire satisfies the boundary-value problem k a2u=au -L < x < L, t > 0, ax2 at'u(-L, t) = u(L, t), t > 0au I =au I t> Oax x= -L ax x=L'u(x, 0) = f(x), -L < x < L,

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