Fréchet Differentiability of the Solution of the Heat Equation with Respect to a Nonlinear Boundary Condition | Zendy

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Fréchet Differentiability of the Solution of the Heat Equation with Respect to a Nonlinear Boundary Condition

Author(s) -

Arnd Rösch

Publication year - 1996

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/718

Subject(s) - nonlinear system , differentiable function , mathematical analysis , mathematics , boundary value problem , boundary (topology) , physics , quantum mechanics

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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