Perturbation of Analytic Semigroups and Applications to Partial\n Differential Equations

2015/05/06 by Martin Adler, Adler, Martin, Miriam Bombieri +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods for differential equations #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1505.01336

openalex publication_date 2015/05/06 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

In a recent paper we presented a general perturbation result for generators\nof C₀-semigroups. The aim of the present paper is to replace, in case the\nunperturbed semigroup is analytic, the various conditions appearing in this\nresult by simpler assumptions on the domain and range of the operators\ninvolved. The power of our result to treat classes of PDE's systematically is\nillustrated by considering a generic example, a degenerate differential\noperator with generalized Wentzell boundary conditions and a reaction diffusion\nequation subject to Neumann boundary conditions with distributed unbounded\ndelay.\n

Citations

• One-parameter semigroups for linear evolution equations

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