Vol. 57, No. 2, 1975

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Nonlinear holomorphic semigroups

Thomas Lee Hayden and Frank Jones Massey

Vol. 57 (1975), No. 2, 423–439
Abstract

Conditions are given on a nonlinear operator A in a Banach space X under which the semigroup, S(t), generated by A has the property that S(t)x is analytic in t for |arg t| < 𝜃 for each fixed x cl(D(A)). Analyticity in t of solutions of u+ Tu = Fu where T generates a linear holomorphic semigroup in X and F maps D(Tα) analytically into X for some α < 1 is also established. These results are applied to establish analyticity in t of solutions to ∂u∕∂t + Lu + β(u) = 0 where β : R R is real analytic, monotone increasing and β(0) = 0, and L is a second order elliptic operator.

Mathematical Subject Classification 2000
Primary: 47H15
Secondary: 35K15
Milestones
Received: 27 February 1974
Revised: 3 March 1975
Published: 1 April 1975
Authors
Thomas Lee Hayden
Frank Jones Massey