Back to Search
Start Over
Well-posedness of second order degenerate integro-differential equations in vector-valued function spaces.
- Source :
- QM - Quaestiones Mathematicae; Jun2015, Vol. 38 Issue 3, p349-368, 20p
- Publication Year :
- 2015
-
Abstract
- We consider the well-posedness of the second order degenerate integrodifferential equations (P2):, (0 ≤ t ≤ 2π) with periodic boundary conditionsu(0) =u(2π), (Mu′)(0) = (Mu′)(2π), in periodic Lebesgue-Bochner spacesLp(𝕋,X), periodic Besov spaces(𝕋,X) and and periodic Triebel-Lizorkin spaces(𝕋,X), whereAandMare closed linear operators on a Banach spaceXsatisfyingD(A) ⊂D(M),a∊L1(ℝ+) andαis a scalar number. Using known operator-valued Fourier multiplier theorems, we give necessary and sufficient conditions for the well-posedness of (P2) in the above three function spaces. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 16073606
- Volume :
- 38
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- QM - Quaestiones Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 103286802
- Full Text :
- https://doi.org/10.2989/16073606.2014.981729