111 citations · 426 across the 46 of their papers we have counts for
7 papers · 2 filters
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}+(-Δ)^{\fracβ{2}} u= I_α(|u|^{p}),\qquad 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 the…
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-…
Fujita-type results for parabolic equations with Hartree-type nonlinearities
Ahmad Z. Fino, Berikbol T. Torebek
This paper investigates the critical behavior of global solutions to a parabolic equation with a Hartree-type nonlinearity of the form $$\left\{\begin{array}{ll} u_{t}+(-Δ)^{\fracβ…
Berezin-Li-Yau inequality for mixed local-nonlocal Dirichlet-Laplacian
Aidyn Kassymov, Berikbol T. Torebek
In this paper, we consider an eigenvalue problem for mixed local-nonlocal Laplacian $$\mathcal{L}^{a,b}_{\Om}:=-aΔ+b(-Δ)^s,\,a>0,\,b\in\mathbb{R},\,s\in (0,1),$$ with Dirichlet bou…
Cazenave-Dickstein-Weissler-type extension of Fujita's problem on Heisenberg groups
Mokhtar Kirane, Ahmad Z. Fino, Berikbol T. Torebek +1
This paper examines the critical exponents for the existence of global solutions to the equation \begin{equation*} \begin{array}{ll} \displaystyle u_t-Δ_{\mathbb{H}}u=\int_0^t(t-s)…
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 …