An improved exponential decay result for some semilinear integrodifferential equations

S. Mazouzi; Nasser-eddine Tatar

Archivum Mathematicum (2003)

  • Volume: 039, Issue: 3, page 163-171
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Mazouzi, S., and Tatar, Nasser-eddine. "An improved exponential decay result for some semilinear integrodifferential equations." Archivum Mathematicum 039.3 (2003): 163-171. <http://eudml.org/doc/249116>.

@article{Mazouzi2003,
abstract = {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.},
author = {Mazouzi, S., Tatar, Nasser-eddine},
journal = {Archivum Mathematicum},
keywords = {semigroup; fractional operator; weakly singular kernels; exponential decay; fractional operator; weakly singular kernels; abstract integrodifferential equation},
language = {eng},
number = {3},
pages = {163-171},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {An improved exponential decay result for some semilinear integrodifferential equations},
url = {http://eudml.org/doc/249116},
volume = {039},
year = {2003},
}

TY - JOUR
AU - Mazouzi, S.
AU - Tatar, Nasser-eddine
TI - An improved exponential decay result for some semilinear integrodifferential equations
JO - Archivum Mathematicum
PY - 2003
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 039
IS - 3
SP - 163
EP - 171
AB - 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.
LA - eng
KW - semigroup; fractional operator; weakly singular kernels; exponential decay; fractional operator; weakly singular kernels; abstract integrodifferential equation
UR - http://eudml.org/doc/249116
ER -

References

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  2. Henry D., Geometric theory of semilinear parabolic equations, Springer-Verlag Berlin, Heidelberg, New York, 1981. (1981) Zbl0456.35001MR0610244
  3. Kirane M., Tatar N.-E., Global existence and stability of some semilinear problems, Arch. Math. (Brno) 36 (2000), 33–44. Zbl1048.34102MR1751612
  4. Mazouzi S., Tatar N.-E., Global existence for some semilinear integrodifferential equations with nonlocal conditions, ZAA 21, No.1 (2002), 249–256. MR1916416
  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. (1997) Zbl0893.26006MR1475574
  6. Medved’ M., Singular integral inequalities and stability of semi-linear parabolic equations, Arch. Math. (Brno) 34 (1998), 183–190. (1998) MR1629697
  7. Michalski M. W., Derivatives of noninteger order and their applications, Dissertationes Mathematicae, Polska Akademia Nauk, Instytut Matematyczny, Warszawa 1993. (1993) Zbl0880.26007MR1247113
  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. (1997) MR1460074
  9. Tatar N.-E., Exponential decay for a semilinear integrodifferential problem with memory, Arab. J. Math. Vol. 7, No. 1 (2001), 29–45. MR1834132

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