Professor Messoud Efendiev, Institute of Computational Biology, Helmholtz Zentrum, Munich, Germany, and Department of Mathematics, TUM, Garching, Germany will give the following seminars:
Seminar 1
Title: Do we have unique profile in asymptotical behaviours?
Time: Tuesday, August 7, 13-14.
Place: Building 303A, auditorium 43
Abstract:
In this talk, I study the asymptotic behavior as x1 → +∞ of solutions of semilinear elliptic equations in quarter- or half-spaces, for which the value at x1 = 0 is given. The uniqueness and characterizations of the one-dimensional or constant profile of the solutions at infinity will be shown. In some cases, we will prove that all solutions u converge at the infinity to the same limiting one -dimensional profile, irrespectively of "initial data". To this end, we prove some new Liouville type results of independent interest for the solutions of some elliptic equations in half-space or in the whole space.
Seminar 2
Title: Dependence of swelling of mitochondria on boundary conditions
Time: Thursday, August 9, 13-14.
Place: Building 303A, auditorium 43
Abstract:
We analyze existence and asymptotic behavior of a system of semilinear diffusion‐reaction equations that arises in the modeling of the mitochondrial swelling process. The model itself expands our previous work in which the mitochondria were assumed to be stationary, whereas now their movement is modeled by linear diffusion. While in the previous model certain formal structural conditions were required for the rate functions describing the swelling process, we show that these are not required in the extended model. Numerical simulations are included to visualize the solutions of the new model and to compare them with the solutions of the previous model.
Those of you interested in one or both of these seminars are mostly welcome.