Some remarks on semi-groups of nonlinear operators
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This article is published in Tohoku Mathematical Journal.The article was published on 1971-01-01 and is currently open access. It has received 47 citations till now.read more
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Journal ArticleDOI
Nonlinear Evolution Equations in Banach Spaces.
TL;DR: In this article, the evolution problem 0∈du/dt+A(t)u(t),u(s)=x, where the A(T) are nonlinear operators acting in a Banach space, is studied.
Journal ArticleDOI
Nonlinear evolution equations in an arbitrary Banach space
TL;DR: In this article, the existence of an evolution operator U(t, s)x 0 corresponding to a weak or generalized solution of the differential equation was proved, and some simple examples were presented.
Book ChapterDOI
Application of Nonlinear Semigroup Theory to Certain Partial Differential Equations
TL;DR: In this article, the authors highlight the applicability of the abstract considerations to several concrete problems, explain what useful information semigroup theory provides and what it does not, and demonstrate how in certain cases, various partial differential equations techniques can be used to extend the theoretical understanding.
Journal ArticleDOI
A generalized domain for semigroup generators
TL;DR: In this paper, a generalized domain D(A) is assigned to each set A such that A+oJl is accretive and R(I+2A)D Cl(D(A)) (where Cl denotes closure) for sufficiently small positive A.
Journal ArticleDOI
Differential equations in a Banach space
S. G. Krein,M. I. Khazan +1 more
TL;DR: A systematic survey of the theory of linear evolution equations in Banach spaces, reviewed in the period 1968-1982 in Ref Zh Matematika, is presented in this paper, with a focus on linear evolution.
References
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Journal ArticleDOI
Generation of semi-groups of nonlinear transformations on general banach spaces,
TL;DR: In this article, the authors continue a discussion of a problem posed by Hille (1951) in a paper titled, "On the Generation of Semigroups and the Theory of Conjugate Functions."
Journal ArticleDOI
Nonlinear semi-groups in Hilbert space
Journal ArticleDOI
Accretive sets and differential equations in Banach spaces
TL;DR: In this article, the authors considered the problem of finding global solutions of the initial value problem (1) in the Banach space, and showed that various approximation processes converge to the solution (whenever it exists).
Journal ArticleDOI
Approximation of semi-groups of nonlinear operators
Isao Miyadera,Shinnosuke Oharu +1 more