Dear Members of the Selection Committee,

I am writing to express my keen interest in participating in the Hong Kong Laureate Forum 2025. I first heard about the Forum through my academic internship at Ghent University, and I was immediately drawn to its mission of fostering dialogue and collaboration among young researchers and distinguished scientists.

I am a PhD student at Nazarbayev University and my research interest is partial differential equations, especially in blow-up phenomena for parabolic equations on exterior domains. Through my studies, I have actively participated in academic conferences (AIMS, UAS, Microlocal Day, Belgium) and my first publication is under review (Journal of Differential Equations). I firmly believe in the importance of making scientific knowledge accessible and inspiring the next generation of researchers. Attending the Hong Kong Laureate Forum would not only enhance my scientific journey but also enable me to share my learnings with a broader community.

I am confident that my academic background, research experience, and enthusiasm for collaboration make me a strong candidate for this exceptional opportunity. I look forward to the possibility of participating in the Forum and contributing to its dynamic intellectual environment.

Thank you for considering my application.

Ghent University

Khoja Akhmet Yassawi International Kazakh-Turkish University

RecLet-prof-Borikhanov.pdf

We investigate the critical behavior of solutions to the semilinear biharmonic heat equation with forcing term $f(x),$ under six homogeneous boundary conditions. This paper is the first since the seminal work by Bandle, Levine, and Zhang [J. Math. Anal. Appl. 251 (2000) 624--648], to focus on the study of critical exponents in exterior problems for semilinear parabolic equations with a forcing term. By employing a method of test functions and comparison principle, we derive the critical exponents $p_{Crit}$ in the sense of Fujita. Moreover, we show that $p_{Crit}=\infty$ if $N=2,3,4$ and $p_{Crit}=\frac{N}{N-4}$ if $N \geq 5$. The impact of the forcing term on the critical behavior of the problem is also of interest, and thus a second critical exponent in the sense of Lee-Ni, depending on the forcing term, is introduced. We also discuss the case $f\equiv 0$ and present the finite-time blow-up results and lifespan estimates of solutions for the subcritical and critical cases. The lifespan estimates of solutions are obtained by employing the method proposed by Ikeda and Sobajama in [Nonlinear Anal. 182 (2019) 57--74].