Article
Strong solution for singularly nonautonomous evolution equation with almost sectorial operators
Author/s | Boldrin Belluzi, Maykel
Caraballo Garrido, Tomás Dias Nascimento, Marcelo José Schiabel, Karina |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2021-08-04 |
Deposit Date | 2023-02-24 |
Published in |
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Abstract | ct. In this paper we consider the singularly nonautonomous evolution
problem
ut + A(t)u = f(t), τ < t < τ + T; u(τ) = u0 ∈ X,
associated with a family of uniformly almost sectorial linear operators A(t) :
D ⊂ X → X, ... ct. In this paper we consider the singularly nonautonomous evolution problem ut + A(t)u = f(t), τ < t < τ + T; u(τ) = u0 ∈ X, associated with a family of uniformly almost sectorial linear operators A(t) : D ⊂ X → X, that is, a family for which a sector of the complex plane is contained in the resolvent of −A(t) and satisfies k(λ + A(t))−1kL(X) ≤ C |λ|α , for some α ∈ (0, 1), uniformly in t. Under a proper condition on the value of α we prove that the linear process associated to the family A(t), t ∈ R, is strongly differentiable and that the singularly nonautonomous problem has a strong solution. An example of a singularly nonautonomous reaction-diffusion equation in a domain with a handle illustrates the abstracts results obtai |
Citation | Boldrin Belluzi, M., Caraballo Garrido, T., Dias Nascimento, M.J. y Schiabel, K. (2021). Strong solution for singularly nonautonomous evolution equation with almost sectorial operators. Discrete and Continuous Dynamical Systems, 43 (1), 177-208. https://doi.org/10.3934/dcds.2022145. |
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