The relativistic Burgers equation on a Friedmann–Lemaître–Robertson–Walker (FLRW) background and its finite volume approximation

Ceylan, Tuba
In this thesis, applications of generalized integral inequalities especially on biomathematics and physics are studied. Application on Biomathematics is about the predatorprey dynamic systems with Beddington DeAngelis type functional response and application on physics is about water percolation equation. This thesis consists 6 chapters. Chapter 1 is introductory and contains the thesis structure. Chapter 2 is about under which conditions the two dimensional predator-prey dynamic system with Beddington DeAngelis type functional response is permenent and globally attractive. Chapter 3 is about the same type dynamic system but with impulses. In that chapter under which conditions the dynamic system has at least one periodic solution is investigated. To get the result we use Continuation Theorem. Using impulse on this type of dynamic system is also important. Because we can model the real life much better by this way. In Chapter 4, the predator-prey dynamic system with Beddington DeAngelis type functional response on periodic time scales in shifts is studied. In this chapter, first we prove which kind of periodic time scales in shifts should be used to find there is at least one δ±-periodic solution for the given system. Then again by using Continuation Theorem we get the desired result. In Chapter 5, first we generalize the Constantin’s Inequality on Nabla and Diamond-α calculus on time scales. Then by using a topological transversality theorem and using the generalization of Constantin’s Inequality on Nabla Calculus, we have showed that the vwater percolation equation on nabla time scales calculus has solution. This solution is unique and bounded. The last chapter is the summary of what we have done in this thesis. As a result, since this study is on time scales, the findings are also important on the discrete and continuous case.