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Preliminaries from functional analysis
Dissipative operators and fractional powers of operators
Semigroup of linear operators
6 other sections not shown
admissible control applying arbitrary element assume assumption Banach space belonging bounded called chapter choose closed operator coefficients complex condition consider constant constructed contained continuously differentiable converges convex Corollary defined Definition denote dense differentiable dissipative operator domain easy eD(A element elliptic equal equation estimate Example exist positive exists expressed extension follows function fundamental solution given gives Hence Hilbert space holds immediately implies independent inequality integral inverse Lemma linear operator mapping neighbourhood normed space obtain particular positive number preceding problem Proof Proposition prove reflexive regular relation Remark replacing respect result right-hand side satisfies semigroup sense sequence shown similar Similarly solution strongly continuous sufficiently Suppose term Theorem topology Un(t uniformly unique values weak weakly πα