16 citations · 71 across the 33 of their papers we have counts for
37 papers
Heat equations driven by mixed local-nonlocal operators with exponential nonlinearity
Dharmendra Kumar Chaurasia, Ahmad Z. Fino, Vishvesh Kumar
We investigate the Cauchy problem for a heat equation driven by the mixed local-nonlocal operator , , with exponential nonlinearity \[ \partial_t…
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…
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 $$\left\{\begin{array}{ll} u_{t}+(-Δ)^{\fracβ…
Nonexistence of global solutions to the Grushin heat equation with nonlocal and local nonlinearities
Ahmad Z. Fino, Arlúcio Viana
In this paper, we investigate the nonexistence of global solutions to the Grushin-type heat equation with nonlinear reaction terms, including cases involving memory effects: $$ \le…
Local and global solvability of the Grushin heat equation with mixed nonlinear memory and reaction terms
Ahmad Z. Fino, Arlucio Viana
In this work, we investigate the solvability of a heat equation involving the Grushin operator. The equation is perturbed by two nonlinear reaction terms, one of which includes a m…
The Fujita exponent for a heat equation with mixed local and nonlocal nonlinearities on the Heisenberg group
Zineb Sabbagh, Ahmad Z. Fino, Mokhtar Kirane
This article deals with the problems of local and global solvability for a semilinear heat equation on the Heisenberg group involving a mixed local and nonlocal nonlinearity. The c…