Nonlinear evolution equations on locally closed graphs

Let X be a real Banach space, let A : D ( A ) ⊆ X ⇝ X be an m -dissipative operator, let I a nonempty, bounded interval And let K : be a given multi-valued function. By using the concept of A-quasi-tangent set introduced by Cârjă, Necula, Vrabie [8] And [9] And using a tangency condition expressed i...

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Published inRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 104; no. 1; pp. 97 - 114
Main Authors Necula, Mihai, Popescu, Marius, Vrabie, Ioan I.
Format Journal Article
LanguageEnglish
Published Milan Springer-Verlag 01.03.2010
Springer Nature B.V
Subjects
Applications of Mathematics
Evolution
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Studies
Theoretical
locally closed graph
Primary 34G25
tangent set
47H20
34C11
multi-valued mapping
Differential inclusion
tangency condition
Secondary 34A60
viability
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Summary:Let X be a real Banach space, let A : D ( A ) ⊆ X ⇝ X be an m -dissipative operator, let I a nonempty, bounded interval And let K : be a given multi-valued function. By using the concept of A-quasi-tangent set introduced by Cârjă, Necula, Vrabie [8] And [9] And using a tangency condition expressed in the terms of this concept, we establish a necessary And sufficient condition for C 0 -viability referring to nonlinear evolution inclusions of the form u ′ ( t ) ∈ Au ( t )+ F ( t, u(t) ), where F is a multi-function defined on the graph of K . As an application, we deduce a comparison result for a class of fully nonlinear evolution inclusions driven by multi-valued perturbations of subdifferentials.
ISSN:1578-7303
1579-1505
DOI:10.5052/RACSAM.2010.10