111 citations · 426 across the 46 of their papers we have counts for
4 papers · 2 filters
Strong gradient absorption and initial decay prevent blow-up
Philippe Souplet, Berikbol T. Torebek
Consider positive classical solutions of the Cauchy problem for , with sufficiently smooth initial data , in the strong absorption regime, namely $q\…
New sharp lifespan estimates for a semilinear heat equation with zero-mass sign-changing initial data
Berikbol T. Torebek
We consider the Cauchy problem $$u_t-Δu=|u|^p,\qquad (t,x)\in(0,T)\times\R^n, \quad u(0,x)=\eps u_0(x),\qquad x\in\R^n,$$ with small sign-changing initial data having zero total ma…
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 + (-Δ)^s u = |x|^{-γ}\,|u|^p, \qquad (t,x)\in(0…
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|^{σ_1}u_t = Δu + |x|^{σ_2}|u|^p + t^\varrho \mathbf{w}(x), \quad (t,x)\in(0,\infty)\times\mathbb{R…