Description
Time scale, arbitrary nonempty closed subset of the real numbers (with the topology and ordering inherited from the real numbers) is an efficient and general framework to study different types of problems to discover the commonalities and highlight the essential differences. Sometimes, we may need to choose an appropriate time scale to establish parallels to known results. We present a few recent results from existence theory of funcational dynamic equations including a few (counter) examples. In particular, we discuss first order functional dynamic equations with delay xDelta(t)=f(t,xt) on a time scale. Here, xt is in Crd([-tau,0],Rn) and is given by xt(s)=x(t+s), -tau < s< 0. We consider an appropriate timescale on which such delay equations can be studied meaningfully. We establish an existence result for the solutions of such problems. We also present a few examples.
Date of Event
February 18, 2016
Location
Mailman-Hollywood Auditorium
NSU News Release Link
http://cnso.nova.edu/news/articles/dynamic-equations.html
Existence Results for Functional Dynamic Equations with Delay
Mailman-Hollywood Auditorium
Time scale, arbitrary nonempty closed subset of the real numbers (with the topology and ordering inherited from the real numbers) is an efficient and general framework to study different types of problems to discover the commonalities and highlight the essential differences. Sometimes, we may need to choose an appropriate time scale to establish parallels to known results. We present a few recent results from existence theory of funcational dynamic equations including a few (counter) examples. In particular, we discuss first order functional dynamic equations with delay xDelta(t)=f(t,xt) on a time scale. Here, xt is in Crd([-tau,0],Rn) and is given by xt(s)=x(t+s), -tau < s< 0. We consider an appropriate timescale on which such delay equations can be studied meaningfully. We establish an existence result for the solutions of such problems. We also present a few examples.
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/10
Presenter Bio
Dr. Bhaskar Tenali joined the Mathematical Sciences department of Florida Tech as associate professor in 2002 and has been a professor since 2007. His main research interests include functional, fuzzy and set differential equations and time scales analysis. Dr. Tenali published about 50 research papers in peer reviewed international journals and co-authored a research monograph on Set Differential Equations. He has supervised the research projects of 20 undergraduate and graduate students for the past 15 years. He supervised the doctoral thesis of six students. He has been a research mentor in a few funded research projects. He has been an invited speaker at several international conferences. Dr. Tenali designed and taught several graduate and undergraduate classes over the past 25 years. He is currently the Chairman of the Academic Policies Committee of the faculty senate at Florida Tech.