Khadijeh Baghaei - Academia.edu (original) (raw)
Papers by Khadijeh Baghaei
Comptes Rendus. Mécanique, 2022
Blow-up, non-extinction and exponential growth of solutions to a fourth-order parabolic equation
Mathematical Methods in the Applied Sciences, 2020
This paper deals with the blow‐up phenomenon to the following quasi‐linear pseudo‐parabolic equat... more This paper deals with the blow‐up phenomenon to the following quasi‐linear pseudo‐parabolic equation with nonlocal source: ut−Δut−∇·(|∇u|2q∇u)=up(x,t)∫ΩK(x,y)up+1(y,t)dy,x,y∈Ω,t>0, where Ω⊆ℝn,n≥3 , is a bounded domain with smooth boundary. Here, 0 < q ≤ p and K(x,y) is an integrable real‐valued function. We show that for q < p, the blow‐up occurs in finite time with suitable initial data and arbitrary positive initial energy. We also state some key results based on the conception of limiting the energy function in the case of nonnegative initial energy. Besides, we obtain the exact blow‐up time under some certain conditions.
Applicable Analysis, 2018
This paper deals with the blow-up phenomenon for a nonlinear wave equation with anisotropy and a ... more This paper deals with the blow-up phenomenon for a nonlinear wave equation with anisotropy and a source term:
Computers & Mathematics with Applications, 2017
This paper is concerned with the blow-up of solutions to a superlinear hyperbolic equation with l... more This paper is concerned with the blow-up of solutions to a superlinear hyperbolic equation with linear damping term u tt − u − ω u t + µu t = |u| p−2 u, in [0, T ] × Ω, where Ω ⊆ R n , n ≥ 1, is a bounded domain with smooth boundary and T > 0. Here, ω ≥ 0 and µ > −ωλ 1 , where λ 1 is the first eigenvalue of the operator − under homogeneous Dirichlet boundary conditions. The recent results show that in the case of ω > 0, if 2 < p < ∞ (n = 1, 2) or 2 < p ≤ 2n n−2 (n ≥ 3), then the solutions to the above equation blow up in a finite time under some suitable conditions on initial data. In this paper, in the case of ω > 0, we obtain a lower bound for the blow-up time when the blow-up occurs. This result extends the recent results obtained by Sun et al. (2014) and Guo and Liu (2016).
Comptes Rendus Mathematique, 2017
Partial differential equations Boundedness of classical solutions for a chemotaxis model with con... more Partial differential equations Boundedness of classical solutions for a chemotaxis model with consumption of chemoattractant Les solutions classiques d'un modèle de chimiotaxie avec consommation de chimioattracteurs sont bornées
Computers & Mathematics with Applications, 2015
Ω |u| p−1 u dx, x ∈ Ω, t > 0, under homogeneous Neumann boundary condition in a bounded domain Ω ... more Ω |u| p−1 u dx, x ∈ Ω, t > 0, under homogeneous Neumann boundary condition in a bounded domain Ω ⊂ R n , n ≥ 1, with smooth boundary. For all p > 1, we prove that the classical solutions to the above equation blow up in finite time when the initial energy is positive and initial data is suitably large. This result improves a recent result by Gao and Han (2011) which asserts the blow-up of classical solutions for n ≥ 3 provided that 1 < p ≤ n+2 n−2 .
In this article, we find a lower bound for the blow-up time of solutions to some nonlinear parabo... more In this article, we find a lower bound for the blow-up time of solutions to some nonlinear parabolic equations under Robin boundary conditions in bounded domains of R^n.
Applicable Analysis, 2014
Mathematical Methods in the Applied Sciences, 2014
Communicated by S. A. Messaoudi This paper deals with the blow-up phenomena for a system of parab... more Communicated by S. A. Messaoudi This paper deals with the blow-up phenomena for a system of parabolic equations with nonlinear boundary conditions. We show that under some conditions on the nonlinearities, blow-up occurs at some finite time. We also obtain upper and lower bounds for the blow-up time when blow-up occurs.
Comptes Rendus Mathematique, 2013
Abstract This paper deals with the blow-up of solutions to some nonlinear divergence form parabol... more Abstract This paper deals with the blow-up of solutions to some nonlinear divergence form parabolic equations with nonlinear boundary conditions. We obtain a lower bound for the blow-up time of solutions in a bounded domain Ω ⊆ R n , n ⩾ 3 .
Comptes Rendus Mathematique, 2013
This work is concerned with a chemotactic model for the dynamics of social interactions between t... more This work is concerned with a chemotactic model for the dynamics of social interactions between two species-foragers u and exploiters v, as well as the dynamics of food resources w consumed by these two species. The foragers search for food directly, while the exploiters head for food by following the foragers. Specifically, the parabolic system in a smoothly bounded convex n-dimensional domain Ω , { ut = ∆u − ∇ • (S 1 (u)∇w), x ∈ Ω , t > 0, vt = ∆v − ∇ • (S 2 (v)∇u), x ∈ Ω , t > 0, wt = d∆w − λ(u + v)w − µw + r(x, t), x ∈ Ω , t > 0, is considered for the constants d, λ, µ > 0 and r ∈ C 0 (Ω × [0, ∞)) with a uniform bound. Volume-filling effects account for a simple version by taking S 1 (u) = u(1 − u), S 2 (v) = v(1 − v). We prove the global existence and boundedness of the unique classical solution to this forager-exploiter model associated with no-flux boundary conditions under the mild assumption that the initial data u 0 , v 0 , w 0 satisfy 0 ≤ u 0 , v 0 ≤ 1 and w 0 ≥ 0.
![Research paper thumbnail of Corrigendum to “Lower bounds for the blow-up time in the higher-dimensional nonlinear divergence form parabolic equations” [C. R. Acad. Sci. Paris, Ser. I 351 (19–20) (2013) 731–735]](https://attachments.academia-assets.com/93700897/thumbnails/1.jpg)
](Comptes Rendus Mathematique, 2014
This corrigendum corrects an unfortunate typographical error that had been forgotten in the above... more This corrigendum corrects an unfortunate typographical error that had been forgotten in the above-mentioned article. Eq. (19) on p. 735 should read: dΦ k 2 + k 1 Φ + k 6 Φ 3(n−2) 3n−8 dt. (19) We thank our readers for their understanding.
Mathematical Methods in the Applied Sciences, 2015
Communicated by M. Groves This paper deals with the blow-up phenomena for a class of fourth-order... more Communicated by M. Groves This paper deals with the blow-up phenomena for a class of fourth-order nonlinear wave equations with a viscous damping term u tt ˛u xxt C u xxxx D f.u x / x , x 2 , t > 0 with D .0, 1/ and˛> 0. Here, f.s/ is a given nonlinear smooth function. For 0 <˛< p 1, we prove that the blow-up occurs in finite time for arbitrary positive initial energy and suitable initial data. This result extends the recent results obtained by Xu et al. (Applicable Analysis)(2013) and Chen and Lu (J. Math. Anal. Appl.
Comptes Rendus. Mécanique, 2022
Blow-up, non-extinction and exponential growth of solutions to a fourth-order parabolic equation
Mathematical Methods in the Applied Sciences, 2020
This paper deals with the blow‐up phenomenon to the following quasi‐linear pseudo‐parabolic equat... more This paper deals with the blow‐up phenomenon to the following quasi‐linear pseudo‐parabolic equation with nonlocal source: ut−Δut−∇·(|∇u|2q∇u)=up(x,t)∫ΩK(x,y)up+1(y,t)dy,x,y∈Ω,t>0, where Ω⊆ℝn,n≥3 , is a bounded domain with smooth boundary. Here, 0 < q ≤ p and K(x,y) is an integrable real‐valued function. We show that for q < p, the blow‐up occurs in finite time with suitable initial data and arbitrary positive initial energy. We also state some key results based on the conception of limiting the energy function in the case of nonnegative initial energy. Besides, we obtain the exact blow‐up time under some certain conditions.
Applicable Analysis, 2018
This paper deals with the blow-up phenomenon for a nonlinear wave equation with anisotropy and a ... more This paper deals with the blow-up phenomenon for a nonlinear wave equation with anisotropy and a source term:
Computers & Mathematics with Applications, 2017
This paper is concerned with the blow-up of solutions to a superlinear hyperbolic equation with l... more This paper is concerned with the blow-up of solutions to a superlinear hyperbolic equation with linear damping term u tt − u − ω u t + µu t = |u| p−2 u, in [0, T ] × Ω, where Ω ⊆ R n , n ≥ 1, is a bounded domain with smooth boundary and T > 0. Here, ω ≥ 0 and µ > −ωλ 1 , where λ 1 is the first eigenvalue of the operator − under homogeneous Dirichlet boundary conditions. The recent results show that in the case of ω > 0, if 2 < p < ∞ (n = 1, 2) or 2 < p ≤ 2n n−2 (n ≥ 3), then the solutions to the above equation blow up in a finite time under some suitable conditions on initial data. In this paper, in the case of ω > 0, we obtain a lower bound for the blow-up time when the blow-up occurs. This result extends the recent results obtained by Sun et al. (2014) and Guo and Liu (2016).
Comptes Rendus Mathematique, 2017
Partial differential equations Boundedness of classical solutions for a chemotaxis model with con... more Partial differential equations Boundedness of classical solutions for a chemotaxis model with consumption of chemoattractant Les solutions classiques d'un modèle de chimiotaxie avec consommation de chimioattracteurs sont bornées
Computers & Mathematics with Applications, 2015
Ω |u| p−1 u dx, x ∈ Ω, t > 0, under homogeneous Neumann boundary condition in a bounded domain Ω ... more Ω |u| p−1 u dx, x ∈ Ω, t > 0, under homogeneous Neumann boundary condition in a bounded domain Ω ⊂ R n , n ≥ 1, with smooth boundary. For all p > 1, we prove that the classical solutions to the above equation blow up in finite time when the initial energy is positive and initial data is suitably large. This result improves a recent result by Gao and Han (2011) which asserts the blow-up of classical solutions for n ≥ 3 provided that 1 < p ≤ n+2 n−2 .
In this article, we find a lower bound for the blow-up time of solutions to some nonlinear parabo... more In this article, we find a lower bound for the blow-up time of solutions to some nonlinear parabolic equations under Robin boundary conditions in bounded domains of R^n.
Applicable Analysis, 2014
Mathematical Methods in the Applied Sciences, 2014
Communicated by S. A. Messaoudi This paper deals with the blow-up phenomena for a system of parab... more Communicated by S. A. Messaoudi This paper deals with the blow-up phenomena for a system of parabolic equations with nonlinear boundary conditions. We show that under some conditions on the nonlinearities, blow-up occurs at some finite time. We also obtain upper and lower bounds for the blow-up time when blow-up occurs.
Comptes Rendus Mathematique, 2013
Abstract This paper deals with the blow-up of solutions to some nonlinear divergence form parabol... more Abstract This paper deals with the blow-up of solutions to some nonlinear divergence form parabolic equations with nonlinear boundary conditions. We obtain a lower bound for the blow-up time of solutions in a bounded domain Ω ⊆ R n , n ⩾ 3 .
Comptes Rendus Mathematique, 2013
This work is concerned with a chemotactic model for the dynamics of social interactions between t... more This work is concerned with a chemotactic model for the dynamics of social interactions between two species-foragers u and exploiters v, as well as the dynamics of food resources w consumed by these two species. The foragers search for food directly, while the exploiters head for food by following the foragers. Specifically, the parabolic system in a smoothly bounded convex n-dimensional domain Ω , { ut = ∆u − ∇ • (S 1 (u)∇w), x ∈ Ω , t > 0, vt = ∆v − ∇ • (S 2 (v)∇u), x ∈ Ω , t > 0, wt = d∆w − λ(u + v)w − µw + r(x, t), x ∈ Ω , t > 0, is considered for the constants d, λ, µ > 0 and r ∈ C 0 (Ω × [0, ∞)) with a uniform bound. Volume-filling effects account for a simple version by taking S 1 (u) = u(1 − u), S 2 (v) = v(1 − v). We prove the global existence and boundedness of the unique classical solution to this forager-exploiter model associated with no-flux boundary conditions under the mild assumption that the initial data u 0 , v 0 , w 0 satisfy 0 ≤ u 0 , v 0 ≤ 1 and w 0 ≥ 0.
Comptes Rendus Mathematique, 2014
This corrigendum corrects an unfortunate typographical error that had been forgotten in the above... more This corrigendum corrects an unfortunate typographical error that had been forgotten in the above-mentioned article. Eq. (19) on p. 735 should read: dΦ k 2 + k 1 Φ + k 6 Φ 3(n−2) 3n−8 dt. (19) We thank our readers for their understanding.
Mathematical Methods in the Applied Sciences, 2015
Communicated by M. Groves This paper deals with the blow-up phenomena for a class of fourth-order... more Communicated by M. Groves This paper deals with the blow-up phenomena for a class of fourth-order nonlinear wave equations with a viscous damping term u tt ˛u xxt C u xxxx D f.u x / x , x 2 , t > 0 with D .0, 1/ and˛> 0. Here, f.s/ is a given nonlinear smooth function. For 0 <˛< p 1, we prove that the blow-up occurs in finite time for arbitrary positive initial energy and suitable initial data. This result extends the recent results obtained by Xu et al. (Applicable Analysis)(2013) and Chen and Lu (J. Math. Anal. Appl.