Loading...

**Search for:**hesaaraki--m

0.004 seconds

#### Lower bounds for the blow-up time of nonlinear parabolic problems with robin boundary conditions

, Article Electronic Journal of Differential Equations ; Vol. 2014 , April , 2014 ; ISSN: 10726691 ; Hesaaraki, M ; Sharif University of Technology
Abstract

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 Rn

#### Lower bounds for the blow-up time in a semilinear parabolic problem involving a variable source

, Article Applied Mathematics Letters ; Vol. 27, issue , 2014 , p. 49-52 ; Ghaemi, M ; Hesaaraki, M ; Sharif University of Technology
Abstract

This letter is concerned with the blow-up of the solutions to a semilinear parabolic problem with a reaction given by a variable exponent. Lower bounds for the time of blow-up are derived if the solutions blow up

#### Lower bounds for the blow-up time in the higher-dimensional nonlinear divergence form parabolic equations

, Article Comptes Rendus Mathematique ; Volume 351, Issue 19-20 , 2013 , Pages 731-735 ; 1631073X (ISSN) ; Hesaaraki, M ; Sharif University of Technology
2013

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⊆Rn, n≥. 3. L'article traite d'un problème d'explosion des solutions d'équations paraboliques non linéaires sous forme de divergence, avec des conditions aux limites non linéaires. On obtient une estimation d'une borne inférieure du temps d'explosion des solutions dans le cas d'un domaine borné Ω⊆Rn, n≥. 3

#### Global existence and boundedness of classical solutions for a chemotaxis model with logistic source

, Article Comptes Rendus Mathematique ; Volume 351, Issue 15-16 , 2013 , Pages 585-591 ; 1631073X (ISSN) ; Hesaaraki, M ; Sharif University of Technology
2013

Abstract

We consider the chemotaxis system:. {ut=δu-∇;{dot operator}(uχ(v)∇;v)+f(u),x∈Ω,t>0,vt=δv-v+ug(u),x∈Ω,t>0, under homogeneous Neumann boundary conditions in a bounded domain Ω⊂Rn, n≥ 1, with smooth boundary and function f is assumed to generalize the logistic source:. f(u)=au-bu2,u≥0, with a>0,b>0. Moreover, χ( s) and g( s) are nonnegative smooth functions and satisfy:. χ(s)≤κ script(1+θ symbols)k,s≥0, with some κ script>0,θ symbol>0 and k>1,g(s)≤h0(1+hs)δ,s≥0,withh0>0,h≥0,δ≥0. We prove that for all positive values of κ script, a and b, classical solutions to the above system are uniformly-in-time bounded. This result extends a recent result by C. Mu, L. Wang, P. Zheng and Q. Zhang (2013)...

#### Blow-up phenomena for a system of semilinear parabolic equations with nonlinear boundary conditions

, Article Mathematical Methods in the Applied Sciences ; Volume 38, Issue 3 , 2015 , Pages 527-536 ; 01704214 (ISSN) ; Hesaaraki, M ; Sharif University of Technology
John Wiley and Sons Ltd
2015

Abstract

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. Copyright

#### Global existence and boundedness of classical solutions to the Owen-Sherratt model

, Article Asian-European Journal of Mathematics ; Volume 9, Issue 1 , 2016 ; 17935571 (ISSN) ; Hesaaraki, M ; Sharif University of Technology
World Scientific Publishing Co. Pte Ltd
2016

Abstract

In this paper, we study the mathematical model proposed by Owen and Sherratt in 1997. We prove that the classical solutions to this model are uniformly-in-time bounded. © World Scientific Publishing Company

#### On existence, non-existence and blow-up results for a singular semilinear laplacian problem

, Article European Journal of Mathematics ; Volume 3, Issue 1 , 2017 , Pages 150-170 ; 2199675X (ISSN) ; Hesaaraki, M ; Sharif University of Technology
Abstract

We study the optimal value of p for solvability of the problem [Equation not available: see fulltext.]Here λ, α> 0 , p> 1 , f is a non-negative measurable function and [InlineEquation not available: see fulltext.], N⩾ 3 , is an open bounded domain with smooth boundary such that 0 ∈ Ω. We find the critical threshold exponent p+(λ, α) for solvability of (1) and show that if [InlineEquation not available: see fulltext.], 1 < p< p+(λ, α) and [InlineEquation not available: see fulltext.] for some sufficiently small c0> 0 , then there exists a solution as a limit of solutions to approximating problems. Moreover, for p⩾ p+(λ, α) we show that a complete blow-up phenomenon occurs. © 2017, Springer...

#### On the existence of fast strong and fast weak ionizing detonation waves in magnetohydrodynamics

, Article Chaos, Solitons and Fractals ; Volume 40, Issue 1 , 2009 , Pages 298-308 ; 09600779 (ISSN) ; Farjami, Y ; Hesaaraki, M ; Sharif University of Technology
2009

Abstract

The existence of structure for ionizing fast-strong and fast-weak detonation waves in magnetohydrodynamics are proved. The reactions are assumed to be one step exothermic reactions with a natural discontinuous reaction rate function. The problem is studied for a general gas, considering some general thermodynamics rules which described by a fairly mild set of hypotheses. The uniqueness and nonuniqueness of structure are also considered. © 2007 Elsevier Ltd. All rights reserved

#### Existence of a unique positive entropy solution to a singular fractional Laplacian

, Article Complex Variables and Elliptic Equations ; 2020 ; Hesaaraki, M ; Sharif University of Technology
Taylor and Francis Ltd
2020

Abstract

In this paper, we study the existence of a positive solution to the elliptic problem: (Formula presented.) Here (Formula presented.) (N>2s) is an open bounded domain with smooth boundary, (Formula presented.) and (Formula presented.). For (Formula presented.), we take advantage of the convexity of Ω. The operator (Formula presented.) indicates the restricted fractional Laplacian, and μ is a non-negative Radon measure as a source term. The assumptions on f and h will be precised later. Besides, we will discuss the notion of entropy solution and its uniqueness for some specific measures. © 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group

#### Periodic solutions for predator-prey systems with Beddington-DeAngelis functional response on time scales

, Article Nonlinear Analysis: Real World Applications ; Volume 9, Issue 3 , 2008 , Pages 1224-1235 ; 14681218 (ISSN) ; Hesaaraki, M ; Sharif University of Technology
2008

Abstract

This paper deals with the question of existence of periodic solutions of nonautonomous predator-prey dynamical systems with Beddington-DeAngelis functional response. We explore the periodicity of this system on time scales. New sufficient conditions are derived for the existence of periodic solutions. These conditions extend previous results presented in [M. Bohner, M. Fan, J. Zhang, Existence of periodic solutions in predator-prey and competition dynamic systems, Nonlinear. Anal.: Real World Appl. 7 (2006) 1193-1204; M. Fan, Y. Kuang, Dynamics of a nonautonomous predator-prey system with the Beddington-DeAngelies functional response, J. Math. Anal. Appl. 295 (2004) 15-39; J. Zhang, J. Wang,...

#### Periodic solutions for a semi-ratio-dependent predator-prey dynamical system with a class of functional responses on time scales

, Article Discrete and Continuous Dynamical Systems - Series B ; Volume 9, Issue 2 , 2008 , Pages 267-279 ; 15313492 (ISSN) ; Hesaaraki, M ; Sharif University of Technology
2008

Abstract

In this paper we explore the existence of periodic solutions of a nonautonomous semi-ratio-dependent predator-prey dynamical system with functional responses on time scales. To illustrate the utility of this work, we should mention that, in our results this system with a large class of monotone functional responses, always has at least one periodic solution. For instance, this system with some celebrated functional responses such as Holling type-II (or Michaelis-Menten), Holling type-III, Ivlev, mx (Holling type I), sigmoidal [e.g., Real and mx2/((A + x)(B +x))] and some other monotone functions, has always at least one ω-periodic solution. Besides, for some well-known functional responses...

#### Periodic solutions for a discrete time predator-prey system with monotone functional responses

, Article Comptes Rendus Mathematique ; Volume 345, Issue 4 , 2007 , Pages 199-202 ; 1631073X (ISSN) ; Hesaaraki, M ; Sharif University of Technology
2007

Abstract

In this Note, sharp sufficient conditions for the existence of periodic solutions of a nonautonomous discrete time semi-ratio-dependent predator-prey system with functional responses are derived. In our results this system with any monotone functional response bounded by polynomials in R+, always has at least one ω-periodic solution. In particular, this system with the most popular functional responses Michaelis-Menten, Holling type-II and III, sigmoidal, Ivlev and some other monotone response functions, always has at least one ω-periodic solution. To cite this article: M. Fazly, M. Hesaaraki, C. R. Acad. Sci. Paris, Ser. I 345 (2007). © 2007 Académie des sciences

#### On the structure of detonation waves in magnetohydrodynamics

, Article Applied Mathematics Research eXpress ; Volume 2006 , 2006 ; 16871200 (ISSN) ; Hesaaraki, M ; Sharif University of Technology
2006

#### A fractional Laplacian problem with mixed singular nonlinearities and nonregular data

, Article Journal of Elliptic and Parabolic Equations ; Volume 7, Issue 2 , 2021 , Pages 787-814 ; 22969020 (ISSN) ; Hesaaraki, M ; Sharif University of Technology
Birkhauser
2021

Abstract

In this note, we study on the existence and uniqueness of a positive solution to the following doubly singular fractional problem: {(-Δ)su=K(x)uq+f(x)uγ+μinΩ,u>0inΩ,u=0in(RN\u03a9).Here Ω ⊂ RN (N> 2 s) is an open bounded domain with smooth boundary, s∈ (0 , 1) , q> 0 , γ> 0 , and K(x) is a positive Hölder continuous function in which behaves as dist (x, ∂Ω) -β near the boundary with 0 ≤ β< 2 s. Also, 0 ≤ f, μ∈ L1(Ω) , or non-negative bounded Radon measures in Ω. Moreover, we assume that 0<βs+q<1, or βs+q>1 with 2 β+ q(2 s- 1) < (2 s+ 1). For s∈(0,12), we take advantage of the convexity of Ω. For any γ> 0 , we will prove the existence of a positive weak (distributional) solution to the above...

#### Existence of a unique positive entropy solution to a singular fractional Laplacian

, Article Complex Variables and Elliptic Equations ; Volume 66, Issue 5 , 2021 , Pages 783-800 ; 17476933 (ISSN) ; Hesaaraki, M ; Sharif University of Technology
Taylor and Francis Ltd
2021

Abstract

In this paper, we study the existence of a positive solution to the elliptic problem: (Formula presented.) Here (Formula presented.) (N>2s) is an open bounded domain with smooth boundary, (Formula presented.) and (Formula presented.). For (Formula presented.), we take advantage of the convexity of Ω. The operator (Formula presented.) indicates the restricted fractional Laplacian, and μ is a non-negative Radon measure as a source term. The assumptions on f and h will be precised later. Besides, we will discuss the notion of entropy solution and its uniqueness for some specific measures. © 2020 Informa UK Limited, trading as Taylor & Francis Group

#### Three-dimensional spread analysis of a Dengue disease model with numerical season control

, Article International Journal of Biomathematics ; Volume 14, Issue 8 , 2021 ; 17935245 (ISSN) ; Hesaaraki, M ; Sharif University of Technology
World Scientific
2021

Abstract

Dengue is among the most important infectious diseases in the world. The main contribution of our paper is to present a mixed system of partial and ordinary differential equations. This combined model is a generalization of the two presented mathematical models (A. L. de Araujo, J. L. Boldrini and B. M. Calsavara, An analysis of a mathematical model describing the geographic spread of dengue disease, J. Math. Anal. Appl. 444 (2016) 298-325) and (L. Cai, X. Li, N. Tuncer, M. Martcheva and A. A. Lashari, Optimal control of a malaria model with asymptomatic class and superinfection, Math. Biosci. 288 (2017) 94-108), describing the geographic spread of dengue disease. Our model has the ability...

#### The singular sources method for an inverse problem with mixed boundary conditions

, Article Journal of Mathematical Analysis and Applications ; Volume 306, Issue 1 , 2005 , Pages 122-135 ; 0022247X (ISSN) ; Hesaaraki, M ; Sharif University of Technology
2005

Abstract

We use the singular sources method to detect the shape of the obstacle in a mixed boundary value problem. The basic idea of the method is based on the singular behavior of the scattered field of the incident point-sources on the boundary of the obstacle. Moreover we take advantage of the scattered field estimate by the backprojection operator. Also we give a uniqueness proof for the shape reconstruction. © 2004 Elsevier Inc. All rights reserved

#### On the structure of ionizing shock waves in magnetofluiddynamics

, Article International Journal of Mathematics and Mathematical Sciences ; Volume 29, Issue 7 , 2002 , Pages 395-415 ; 01611712 (ISSN) ; Hesaaraki, M ; Sharif University of Technology
2002

Abstract

Ionizing shock waves in magnetofluiddynamics occur when the coefficient of electrical conductivity is very small ahead of the shock and very large behind it. For planner motion of plasma, the structure of such shock waves are stated in terms of a system of four-dimensional equations. In this paper, we show that for the above electrical conductivity as well as for limiting cases, that is, when this coefficient is zero ahead of the shock and/or is infinity behind it, ionizing fast, slow, switch-on and switch-off shocks admit structure. This means that physically these shocks occur. © 2002 Hindawi Publishing Corporation. All rights reserved

#### Existence of positive solution for nonlocal singular fourth order Kirchhoff equation with Hardy potential

, Article Positivity ; Volume 21, Issue 4 , 2017 , Pages 1545-1562 ; 13851292 (ISSN) ; Vaezpour, S. M ; Hesaaraki, M ; Sharif University of Technology
Abstract

This paper is concerned with the existence of positive solution to a class of singular fourth order elliptic equation of Kirchhoff type (Formula Presented.)▵2u-λM(‖∇u‖2)▵u-μ|x|4u=h(x)uγ+k(x)uα,under Navier boundary conditions, u= ▵u= 0. Here Ω⊂ RN, N≥ 1 is a bounded C4-domain, 0 ∈ Ω, h(x) and k(x) are positive continuous functions, γ∈ (0 , 1) , α∈ (0 , 1) and M: R+→ R+ is a continuous function. By using Galerkin method and sharp angle lemma, we will show that this problem has a positive solution for m0 and 0 < μ< μ∗. Here μ∗=(N(N-4)4)2 is the best constant in the Hardy inequality. Besides, if μ= 0 , λ> 0 and h, k are Lipschitz functions, we show that this problem has a positive smooth...

#### Nonlocal Lazer–McKenna-type problem perturbed by the Hardy’s potential and its parabolic equivalence

, Article Boundary Value Problems ; Volume 2021, Issue 1 , 2021 ; 16872762 (ISSN) ; Hesaaraki, M ; Karim Hamdani, M ; Thanh Chung, N ; Sharif University of Technology
Springer Science and Business Media Deutschland GmbH
2021

Abstract

In this paper, we study the effect of Hardy potential on the existence or nonexistence of solutions to the following fractional problem involving a singular nonlinearity: {(−Δ)su=λu|x|2s+μuγ+fin Ω,u>0in Ω,u=0in (RN∖Ω). Here 0 < s< 1 , λ> 0 , γ> 0 , and Ω ⊂ RN (N> 2 s) is a bounded smooth domain such that 0 ∈ Ω. Moreover, 0 ≤ μ, f∈ L1(Ω). For 0 < λ≤ Λ N,s, Λ N,s being the best constant in the fractional Hardy inequality, we find a necessary and sufficient condition for the existence of a positive weak solution to the problem with respect to the data μ and f. Also, for a regular datum of f, under suitable assumptions, we obtain some existence and uniqueness results and calculate the rate of...