We consider the heat equation with a nonlinear function a in the boundary condition depending on the boundary values of the solution u of the initial-boundary value problem only and belonging to a set of admissible differentiable or uniformly Lipschitz continuous functions. For this problem Lipschitz continuity and Fréchet differentiability of the mapping under different assumptions are derived.
Cite this article
Arnd Rösch, Fréchet Differentiability of the Solution of the Heat Equation with Respect to a Nonlinear Boundary Condition. Z. Anal. Anwend. 15 (1996), no. 3, pp. 603–618DOI 10.4171/ZAA/718