Previous |  Up |  Next


semigroup; fractional operator; weakly singular kernels; exponential decay
We prove exponential decay for the solution of an abstract integrodifferential equation. This equation involves coefficients of polynomial type, weakly singular kernels as well as different powers of the unknown in some norms.
[1] Balasubramaniam P., Chandrasekaran M.: Existence of solutions of nonlinear integrodifferential equations with nonlocal boundary conditions in Banach spaces. Atti Sem. Math. Fis. Univ. Modena XLVI (1998), 1–13. MR 1628648
[2] Henry D.: Geometric theory of semilinear parabolic equations. Springer-Verlag Berlin, Heidelberg, New York, 1981. MR 0610244 | Zbl 0456.35001
[3] Kirane M., Tatar N.-E.: Global existence and stability of some semilinear problems. Arch. Math. (Brno) 36 (2000), 33–44. MR 1751612 | Zbl 1048.34102
[4] Mazouzi S., Tatar N.-E.: Global existence for some semilinear integrodifferential equations with nonlocal conditions. ZAA 21, No.1 (2002), 249–256. MR 1916416
[5] Medved’ M.: A new approach to an analysis of Henry type integral inequalities and their Bihari type versions. J. Math. Anal. Appl. 214 (1997), 349–366. MR 1475574 | Zbl 0893.26006
[6] Medved’ M.: Singular integral inequalities and stability of semi-linear parabolic equations. Arch. Math. (Brno) 34 (1998), 183–190. MR 1629697
[7] Michalski M. W.: Derivatives of noninteger order and their applications. Dissertationes Mathematicae, Polska Akademia Nauk, Instytut Matematyczny, Warszawa 1993. MR 1247113 | Zbl 0880.26007
[8] Ntouyas S. K., Tsamatos P. Ch.: Global existence for semilinear evoluton integrodifferential equations with delay and nonlocal conditions. Appl. Anal. 64 (1997), 99–105. MR 1460074
[9] Tatar N.-E.: Exponential decay for a semilinear integrodifferential problem with memory. Arab. J. Math. Vol. 7, No. 1 (2001), 29–45. MR 1834132
Partner of
EuDML logo