Date:
Speaker: Joel E. Restrepo, Department of Mathematics, CINVESTAV, Mexico City, Mexico
Time : 10:00 - 11.00 CEST (Rome/Paris)
Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy
Zoom link : A link will appear here, one hour before the talk
Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)
* SISSA, International School of Advanced Studies, Italy
** Eastern Mediterranean University, Northern Cyprus
Keywords: Abstract wave type equations, Almost sectorial operators, Classical solutions, Non-local operators in time
Abstract: We study homogeneous and non-homogeneous abstract wave type equations by using a non-local operator in time and an almost sectorial operator in space. For the latter kind of operators, we do not need to have dense domains and/or ranges. We find the explicit solution operators in both cases. Moreover, we show that indeed they are classical solutions. Some examples are given to illustrate the main results. Some of the main ideas are derived from [1, 2, 3, 4, 5, 6].
Biography: Joel E. Restrepo is a Colombian mathematician and is a researcher in the Department of Mathematics of Center for Research and Advanced Studies of the National Polytechnic Institute, Mexico City, Mexico. Previously, I was a postdoctoral researcher at different research centers in Belgium, Russia and Kazakhstan. He has carried out mathematical research in a variety of topics connecting different areas of mathematics. My research links several techniques in complex analysis, operator theory, harmonic analysis, PDEs, etc. He also has participated in many international conferences, seminars and other related events and has been involved in the organization of several of these scientific projects as well. .
Bibliography
[2] G. Da Prato. Semigruppi di crescenca n. Ann. Scuola Norm. Sup. Pisa, 20(3), (1966), 753–782.
[3] F. Periago, B. Straub. A functional calculus for almost sectorial operators and applications to abstract evolution equations. J. Evol. Equ., 2, (2002), 41–68.
[4] P.E. Sobolevskiˇi. On semigroups of growth α. Dokl. Akad. Nauk SSSR, 196(3), (1971), 535–537.
[5] R-N. Wang, D-H. Chen, T-J. Xiao. Abstract fractional Cauchy problems with almost sectorial operators. J. Differ. Equ. 252(1), (2012), 202–235.
[6] A.V. Zafievskiˇi. On semigroups with singularities summable with a power-weight at zero. Soviet Math. Dokl., 11(6), (1970), 1408–1411.
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