H. Altamimi | Searcharxiv

arXiv2024

Subordinators and generalized heat kernels: Random time change and long time dynamics

This paper focuses on studying the long-time dynamics of the subordination process for a range of linear evolution equations, with a special emphasis on the fractional heat equation. By treating inverse subordinators as random time variables and employing the subordination principle to solve forward Kolmogorov equations, we explore the behavior of the solutions over extended periods. We provide a detailed description of the specific classes of subordinators suitable for conducting asymptotic analysis. Our findings not only extend existing research, but also enhance the results previously presented in [9, 10].

math.AP↗

arXiv2022

On the Fujita exponent for a nonlinear parabolic equation with a forcing term

The purpose of this work is to analyze the blow-up of solutions of the nonlinear parabolic equation \[ u_t-\Delta u=|x|^{\alpha}|u|^{p}+{\mathtt a}(t)\textbf{w}(x) \ \quad\mbox{for } (t,x)\in(0,\infty)\times\mathbb{R}^{N}, \] where $p>1$, $\alpha\in\mathbb{R}$ and ${\mathtt a}$, $\textbf{w}$ are suitable given functions. We improve earlier results by considering a wide class of functions ${\mathtt a}(t)$.

math.AP↗