Access the full text.
Sign up today, get DeepDyve free for 14 days.
I. Kmit, N. Lyul’ko (2016)
Perturbations of superstable linear hyperbolic systemsarXiv: Analysis of PDEs
R. Rosenbaum (1950)
Sub-additive functionsDuke Mathematical Journal, 17
(2001)
Smart structures and super stability, in Evolution Equations and Their Applications in Physical and Life Sciences
E. Davies (1980)
One-parameter semigroups
(1983)
Semigroups of Linear Operators and Applications to Partial Differential Equations
Jian-Hua Chen, Nian-yu Yi, Yongyong Li (2018)
Exponential stability of perturbed superstable systems in Hilbert spacesSemigroup Forum, 96
V. Balakrishnan.A. (1997)
On Superstability of Semigroups
Jian-Hua Chen, Wen-Ying Lu (2011)
Perturbation of nilpotent semigroups and application to heat exchanger equationsAppl. Math. Lett., 24
(1998)
On the solvability of the problem with a nonlocal integral condition for differential equation in a Banach space, Differ
K. Engel, R. Nagel (1999)
One-parameter semigroups for linear evolution equationsSemigroup Forum, 63
Vu Tung (2018)
Special Examples of Superstable Semigroups and Their Application in the Inverse Problems Theory, 18
(1969)
Priblizhennoe reshenie operatornykh uravnenii (Approximate Solution of Operator Equations)
A. Bruckner (1962)
Tests for superadditivity of functions, 13
A. Prilepko (2005)
The Semigroup Method for Inverse, Nonlocal, and Nonclassical Problems. Prediction-Control and Prediction-Observation for Evolution Equations: IDifferential Equations, 41
(1967)
Lineinye differentsial’nye uravneniya v banakhovom prostranstve (Linear Differential Equations in a Banach Space)
D. Creutz, M. Mazo, C. Preda (2009)
SUPERSTABILITY AND FINITE TIME EXTINCTION FOR C0-SEMIGROUPSarXiv: Functional Analysis
(1967)
Translated under the title
(2018)
On solvability of nonlocal problem for evolution equation with a superstable semigroup, in Nek. aktual. probl. sovrem. mat. mat. obraz.: mater. nauchn. konf
(1974)
Teoriya funktsii veshchestvennoi peremennoi (Theory of Functions of Real Variable)
I. Tikhonov, Тихонов Владимирович, S. Nguyen, Ву Тунг (2018)
The Solvability of the Inverse Problem for the Evolution Equation with a Superstable Semigroup, 26
S. Rathore (1965)
On Subadditive and Superadditive FunctionsAmerican Mathematical Monthly, 72
A. Balakrishnan (2005)
Superstability of systemsAppl. Math. Comput., 164
A. Bruckner (1960)
Minimal superadditive extensions of superadditive functionsPacific Journal of Mathematics, 10
(2020)
Solvability of the model nonlocal problem assoaciated with the general neutron transport equation
C. Preda (2017)
On the Roughness of Quasinilpotency Property of One-parameter SemigroupsCanadian Mathematical Bulletin, 60
I. Tikhonov (2003)
Uniqueness theorems for linear non-local problems for abstract differential equationsIzvestiya: Mathematics, 67
R. Cooke (1949)
Functional Analysis and Semi-GroupsNature, 163
A. Bruckner, E. Ostrow (1962)
SOME FUNCTION CLASSES RELATED TO THE CLASS OF CONVEX FUNCTIONSPacific Journal of Mathematics, 12
We study a linear nonlocal problem for an evolution equation in a Banach space. Thestandard semigroup approach is used but integral averaging over time is used instead of thetraditional initial condition. It is assumed that the evolution semigroup associated with theabstract differential equation is superstable (quasinilpotent), i.e., has an infinite negativeexponential type. A theorem about unique solvability of the posed nonlocal problem is proved. Itis shown that the solution can be represented by a convergent Neumann series. Some corollariesare noted. The case in which the semigroup is nilpotent is treated separately. The class ofexamples of superstable semigroups that are of interest in mathematical physics is outlined.
Differential Equations – Springer Journals
Published: Apr 1, 2020
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.