12 papers
Sharp Lifespan Estimates and Fujita Phenomena for Fractional Hardy-Hénon Type Parabolic Equations
Mohamed Majdoub, Berikbol T. Torebek
We study the lifespan of mild solutions to the fractional semilinear parabolic Cauchy problem with a Hardy--Hénon-type weight \[ u_t + (-Î)^s u = |x|^{-γ}\,|u|^p, \qquad (t,x)\i…
A note on lifespan estimates for higher-order parabolic equations
Nurdaulet N. Tobakhanov, Berikbol T. Torebek
We investigate the lifespan of solutions to the higher-order semilinear parabolic equation with initial data. We focus on th…
Forcing Effects on Finite-Time Blow-Up in Degenerate and Singular Parabolic Equations
Mohamed Majdoub, Berikbol T. Torebek
We study the degenerate and singular parabolic equation with a forcing term \[ |x|^{Ï_1}u_t = Îu + |x|^{Ï_2}|u|^p + t^\varrho \mathbf{w}(x), \quad (t,x)\in(0,\infty)\times\mathb…
Parabolic problems whose Fujita critical exponent is not given by scaling
Ahmad Z. Fino, Berikbol T. Torebek
This paper investigates the (fractional) heat equation with a nonlocal nonlinearity involving a Riesz potential: \begin{equation*} u_{t}+(-Î)^{\fracβ{2}} u= I_α(|u|^{p}),\qquad…
Fujita-type results for the semilinear heat equations driven by mixed local-nonlocal operators
Vishvesh Kumar, Berikbol T. Torebek
This paper explores the critical behavior of the semilinear heat equation , considering both the presence and absence of a forcing term …
Blow-up criteria for the semilinear parabolic equations driven by mixed local-nonlocal operators
Vishvesh Kumar, Berikbol T. Torebek
The main goal of this paper is to establish \emph{necessary and sufficient conditions} for the nonexistence of a global solution to the semilinear heat equation with a mixed local-…