Generalized diffusion problems in a conical domain, part II
Rabah Labbas (LMAH), St\'ephane Maingot (LMAH), Alexandre Thorel, (LMAH)
TL;DR
This paper investigates the mathematical properties of generalized diffusion problems in conical domains by analyzing the invertibility of sums of linear operators using established functional analysis strategies.
Contribution
It provides a comprehensive study of the sum of linear operators in Banach spaces for diffusion problems, extending previous work with new analytical techniques.
Findings
Successful application of Da Prato-Grisvard strategy
Application of Dore-Venni approach to the problem
Complete analysis of operator sums in Banach spaces
Abstract
After different variables and functions changes, the generalized dispersal problem, recalled in (1) below and considered in part I, see [14], leads us to invert a sum of linear operators in a suitable Banach space, see (2) below. The essential result of this second part lies in the complete study of this sum using the two well-known strategies: the one of Da Prato-Grisvard [4] and the one of Dore-Venni [6].
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Taxonomy
TopicsDifferential Equations and Numerical Methods · Differential Equations and Boundary Problems · Nonlinear Differential Equations Analysis