111 citations · 426 across the 46 of their papers we have counts for
50 papers
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…
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 …
Blow-up results for the semilinear Schrödinger equations with forcing and gradient terms: the critical cases
Berikbol T. Torebek
The paper is devoted to the study of critical cases of the nonlinear Schrödinger (NLS) equation with source and gradient terms, subsequently providing answers to some open question…
On the critical behavior for the semilinear biharmonic heat equation with forcing term in an exterior domain
Nurdaulet N. Tobakhanov, Berikbol T. Torebek
In this paper, we investigate the critical behavior of solutions to the semilinear biharmonic heat equation with forcing term under six homogeneous boundary conditions. Thi…
Higher order hypoelliptic damped wave equations on graded Lie groups with data from negative order Sobolev spaces: the critical case
Vishvesh Kumar, Shyam Swarup Mondal, Michael Ruzhansky +1
Let be a graded Lie group with homogeneous dimension . In this paper, we study the Cauchy problem for a semilinear hypoelliptic damped wave equation involving a posi…
Behavior of solutions to semilinear evolution inequalities in an annulus: the critical cases
Meiirkhan B. Borikhanov, Berikbol T. Torebek
In the present paper, we consider the parabolic and hyperbolic inequalities with a singular potentials and with a critical nonlinearities in the annulus domain. The problems are st…
Integro-differential diffusion equations on graded Lie groups
Joel E. Restrepo, Michael Ruzhansky, Berikbol T. Torebek
We first study the existence, uniqueness and well-posedness of a general class of integro-differential diffusion equation on , is a gra…
Semilinear wave inequalities with double damping and potential terms on Riemannian Manifolds
Mohamed Jleli, Michael Ruzhansky, Bessem Samet +1
We study a semilinear wave inequality with double damping on a complete noncompact Riemannian manifold. The considered problem involves a potential function depending on the sp…
Global behavior of nonlocal in time reaction-diffusion equations
Berikbol T. Torebek
The present paper considers the Cauchy-Dirichlet problem for the time-nonlocal reaction-diffusion equation $$\partial_t (k\ast(u-u_0))+\mathcal{L}_x [u]=f(u),\,\,\,\, x\inΩ\subset\…
Fujita-type results for the degenerate parabolic equations on the Heisenberg groups
Ahmad Z. Fino, Michael Ruzhansky, Berikbol T. Torebek
In this paper, we consider the Cauchy problem for the degenerate parabolic equations on the Heisenberg groups with power law non-linearities. We obtain Fujita-type critical exponen…
Instantaneous blow up solutions for nonlinear Sobolev type equations on the Heisenberg Group
Meiirkhan B. Borikhanov, Michael Ruzhansky, Berikbol T. Torebek
In this paper, we study the nonlinear Sobolev type equations on the Heisenberg group. We show that the problems do not admit nontrivial local weak solutions, i.e. "instantaneous bl…
On inhomogeneous exterior Robin problems with critical nonlinearities
Meiirkhan B. Borikhanov, Berikbol T. Torebek
The paper studies the large-time behavior of solutions to the Robin problem for PDEs with critical nonlinearities. For the considered problems, nonexistence results are obtained, w…
Critical exponents for the -Laplace heat equations with combined nonlinearities
Berikbol T. Torebek
This paper studies the large-time behavior of solutions to the quasilinear inhomogeneous parabolic equation with combined nonlinearities. This equation is a natural extension of th…
Decay estimates for the time-fractional evolution equations with time-dependent coefficients
Asselya G. Smadiyeva, Berikbol T. Torebek
In this paper, the initial-boundary value problems for the time-fractional degenerate evolution equations are considered. Firstly, in the linear case, we obtain the optimal rates o…
Nonexistence of global solutions for an inhomogeneous pseudo-parabolic equation
Meiirkhan B. Borikhanov, Berikbol T. Torebek
In the present paper, we study an inhomogeneous pseudo-parabolic equation with nonlocal nonlinearity $$u_t-kΔu_t-Δu=I^γ_{0+}(|u|^{p})+ω(x),\,\ (t,x)\in(0,\infty)\times\mathbb{R}^N,…