Integrated semigroups and parabolic equations. Part I: linear perburbation of almost sectorial operators |
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| Authors: | Arnaud Ducrot Pierre Magal Kevin Prevost |
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| Institution: | 1. UMR CNRS 5251 IMB and INRIA Bordeaux sud-ouest Anubis, Université de Bordeaux, 3 place de la Victoire, 33000, Bordeaux, France
2. Department of Mathematics, University of Le Havre, 25 rue philippe Lebon, 76058, Le Havre, France
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| Abstract: | The paper deals with linear abstract Cauchy problem with non-densely defined and almost sectorial operators, whenever the
part of this operator in the closure of its domain is sectorial. This kind of problem naturally arises for parabolic equations
with non-homogeneous boundary conditions. Using the integrated semigroup theory, we prove an existence and uniqueness result
for integrated solutions. Moreover, we study the linear perturbation problem. |
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