On the class of nonlinear evolution operators in Banach space

1986 ◽  
Vol 10 (4) ◽  
pp. 315-337 ◽  
Author(s):  
Toshiyuki Iwamiya ◽  
Shinnosuke Oharu ◽  
Tadayasu Takahashi
Keyword(s):  
Banach Space ◽  
Nonlinear Evolution ◽  
Evolution Operators

scholarly journals On some dichotomy concepts with different growth rates for evolution operators in Banach spaces

2015 ◽  
Vol 53 (2) ◽  
pp. 133-150
Author(s):  
Nicolae Marian Seimeanu
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Growth Rates ◽  
Real Numbers ◽  
Evolution Operators

Abstract This paper treats three concepts of (h, k)-dichotomy and their correspondents in the uniform cases. The connections between them are established through examples and counterexamples presented on the Banach space of square-summable sequences of real numbers.

scholarly journals Nonlinear Evolution Equations with Exponentially Decaying Memory: Existence via Time Discretisation, Uniqueness, and Stability

2020 ◽  
Vol 20 (1) ◽  
pp. 89-108 ◽  
Author(s):  
André Eikmeier ◽  
Etienne Emmrich ◽  
Hans-Christian Kreusler
Keyword(s):  
Banach Space ◽  
Integral Operator ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Inner Product ◽  
Initial Value ◽  
Time Discretisation ◽  
Volterra Integral Operator ◽  
Stability Results

AbstractThe initial value problem for an evolution equation of type {v^{\prime}+Av+BKv=f} is studied, where {A:V_{A}\to V_{A}^{\prime}} is a monotone, coercive operator and where {B:V_{B}\to V_{B}^{\prime}} induces an inner product. The Banach space {V_{A}} is not required to be embedded in {V_{B}} or vice versa. The operator K incorporates a Volterra integral operator in time of convolution type with an exponentially decaying kernel. Existence of a global-in-time solution is shown by proving convergence of a suitable time discretisation. Moreover, uniqueness as well as stability results are proved. Appropriate integration-by-parts formulae are a key ingredient for the analysis.

scholarly journals Connections between Some Concepts of Polynomial Trichotomy for Noninvertible Evolution Operators in Banach Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Mihai-Gabriel Babuţia ◽  
Nicolae Marian Seimeanu
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Evolution Operators

The present paper treats three concepts of nonuniform polynomial trichotomies for noninvertible evolution operators acting on Banach spaces. The connections between these concepts are established through numerous examples and counterexamples for systems defined on the Banach space of square-summable sequences.

scholarly journals Nonlinear evolution operators in a Frechet space

1984 ◽  
Vol 10 (2) ◽  
pp. 243-270
Author(s):  
Kazuo KOBAYASI ◽  
Shinnosuke OHARU
Keyword(s):  
Nonlinear Evolution ◽  
Fréchet Space ◽  
Frechet Space ◽  
Evolution Operators
Sign in / Sign up

Export Citation Format

Share Document