Title

The heat equation with generalized Wentzell boundary condition

Abstract

Let Ω be a bounded subset of RN, a ε C1 (Ω) with a > 0 in Ω and A be the operator defined by Au := ∇ · (a∇u) with the generalized Wentzell boundary condition equation presented If ∂Ω is in C2, β and γ are nonnegative functions in C1 (∂Ω), with β > 0, and Γ := {x ε ∂Ω : a(x) > 0] ≠ ø, then we prove the existence of a (Co) contraction semigroup generated by Ā, the closure of A, on a suitable Lp space, 1 ≤ p < ∞ and on C(Ω). Moreover, this semigroup is analytic if 1 < p < ∞.

Publication Title

Journal of Evolution Equations

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