Strong solution for singularly nonautonomous evolution equation with almost sectorial operators
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...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/142975 |
| Acceso en línea: | https://hdl.handle.net/11441/142975 https://doi.org/10.3934/dcds.2022145 |
| Access Level: | acceso abierto |
| Palabra clave: | Singularly nonautonomous parabolic problems almost sectorial operators regularization smoothing effect |
| Sumario: | 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 |
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