Khompysh Khonatbek (Al-Farabi Kazakh National University, Kazakhstan) – Inverse Source Problems for Nonlinear Evolution Equations

In this talk, I will discuss inverse source problems for nonlinear evolution equations, particularly for parabolic and pseudoparabolic equations perturbed by p-Laplacian diffusion and power-law reaction terms. We also consider inverse problems for these equations with time-fractional derivatives. Such parabolic and pseudoparabolic equations, modified by p-Laplacian diffusion and power-law reaction terms, have various applications—for instance, in modeling non-Newtonian fluids, filtration processes, and more.

For all these problems, we establish sufficient conditions on the data that guarantee the existence and uniqueness of weak solutions to the given problems. In addition, we obtain some qualitative properties of the solutions, such as extinction in finite time, large time behavior, etc.