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Well-Posedness and Spectral Analysis of Integrodifferential Equations Arising in Viscoelasticity Theory
- Source :
- Journal of Mathematical Sciences. 233:555-577
- Publication Year :
- 2018
- Publisher :
- Springer Science and Business Media LLC, 2018.
-
Abstract
- We study the well-posedness of initial-value problems for abstract integrodifferential equations with unbounded operator coefficients in Hilbert spaces and provide a spectral analysis of operator functions that are symbols of the specified equations. These equations represent an abstract form of linear partial integrodifferential equations arising in viscoelasticity theory and other important applications. For the said integrodifferential equations, we obtain well-posedness results in weighted Sobolev spaces of vector functions defined on the positive semiaxis and valued in a Hilbert space. For the symbols of the said equations, we find the localization and the structure of the spectrum.
- Subjects :
- Statistics and Probability
Unbounded operator
Quantitative Biology::Neurons and Cognition
Applied Mathematics
General Mathematics
Operator (physics)
010102 general mathematics
Mathematical analysis
Spectrum (functional analysis)
Hilbert space
Banach space
Space (mathematics)
01 natural sciences
010101 applied mathematics
Sobolev space
symbols.namesake
symbols
0101 mathematics
Vector-valued function
Mathematics
Subjects
Details
- ISSN :
- 15738795 and 10723374
- Volume :
- 233
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematical Sciences
- Accession number :
- edsair.doi...........d779f965fbcdf27fae6b1b69144f78ef