Graduate Student Seminar

Speaker: Mr. Tahir Bacha Issa

Title: Dynamics in chemotaxis models of parabolic-elliptic type on bounded domain with time and space dependent logistic sources

Abstract: In this talk, we will consider the dynamics of a chemotaxis model of parabolic-elliptic type with local as well as nonlocal time and space dependent logistic source on bounded domain. We first prove the local existence and uniqueness of classical solutions for various initial functions. Next, under some conditions on the coefficients, the chemotatic sensitivity and the dimension of the space, we prove the global existence and boundedness of classical solutions with given nonnegative initial function. Then, under the same conditions for the global existence, we show that the system has an entire positive classical solution. Moreover, if the coefficients are periodic in time or are independent of time, then the system has a time periodic positive solution with same period as the coefficients or a steady state positive solution. Furthermore, if the coefficients are spatially homogeneous, then the system has a spatially homogeneous entire positive solution. Finally, under some further assumptions, we prove that the system has a unique entire positive solution which is globally stable. Moreover, if the coefficients are periodic or almost periodic in time, then the unique entire positive solution is also periodic or almost periodic in time.