Fréchet Differentiability of the Solution of the Heat Equation With Respect to a Nonlinear Boundary Condition
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چکیده
Fr echet diierentiability of the solution of the heat equation with respect to a nonlinear boundary condition Arnd RR osch Abstract. Consider the heat equation with a nonlinear function in the boundary condition which depends only on the boundary values x of the solution u of the initial-boundary value problem. The function belongs to a set of admissible diierentiable or uniformly Lipschitz continuous functions. For this problem Lipschitz continuity and Fr echet diierentiability of the mapping 7 ! x under diierent assumptions are derived.
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تاریخ انتشار 1996