排序方式: 共有7条查询结果,搜索用时 15 毫秒
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Boumediene Abdellaoui Sofiane E. H. Miri Ireneo Peral Tarik M. Touaoula 《NoDEA : Nonlinear Differential Equations and Applications》2014,21(4):453-490
In this paper we deal with the following quasilinear parabolic problem $$\left\{\begin{array}{l@{\quad}l} (u^\theta)_t - \Delta_p {u} = \lambda \frac{u^{p - 1}}{|x|^{p}} + u^q + f,\,\, u \geq 0 \quad {\rm in} \;\;\Omega \times (0, T),\\ u(x, t) = 0 \quad\qquad\qquad\qquad\qquad\qquad\qquad {\rm on}\; \partial \Omega \times(0, T),\\ u(x, 0) = u_0(x), \,\,\, \qquad\qquad\qquad\qquad\qquad x \in\; \Omega,\end{array}\right.$$ where θ is either 1 or (p ? 1), \({N \geq 3, \,\Omega \subset \mathcal{IR}^N}\) is either a bounded regular domain containing the origin or \({\Omega \equiv \mathcal{IR}^N}\) , 1 < p < N, q > 0 and u 0 ≥ 0, f ≥ 0 with suitable hypotheses. The aim of this work is to get natural conditions to show the existence or the nonexistence of nonnegative solutions. In the case of nonexistence result, we analyze blow-up phenomena for approximated problems in connection with the classical Harnack inequality, in the Moser sense, more precisely in connection with a strong maximum principle. We also study when finite time extinction (1 < p < 2) and finite speed propagation (p > 2) occur related to the reaction power. 相似文献
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The aim of this work is to establish the existence of multi-peak solutions for the following class of quasilinear problems where \(\epsilon\) is a positive parameter, \(N\geq2\), \(V\), \(f\) are continuous functions satisfying some technical conditions and \(\phi\) is a \(C^{1}\)-function.
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$$ - \mbox{div} \bigl(\epsilon^{2}\phi\bigl(\epsilon|\nabla u|\bigr)\nabla u \bigr) + V(x)\phi\bigl(\vert u\vert\bigr)u = f(u)\quad\mbox{in } \mathbb{R}^{N}, $$
3.
Boumediene Abdellaoui Tarik Mohamed Touaoula 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(3):271-288
In this paper we consider age structured equation with diffusion under nonlocal boundary condition and nonnegative initial
data. We prove existence, uniqueness and the positivity of the solution to the above problem. Our main result is to get an
exponential decay of the solution for large times toward such a study state. To this end we prove a weighted Poincaré–Wirtinger’s
type inequality in unbounded domain. 相似文献
4.
We establish a priori estimates for solutions to ultraparabolic equations which play a crucial role in the solvability of
the initial value problem. A class of these equations came from population dynamics, namely from a fish larvae model.
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5.
Mohamed Nor Frioui Sofiane El-hadi Miri Tarik Mohamed Touaoula 《Journal of Applied Mathematics and Computing》2018,58(1-2):47-73
The aim of this paper is to provide a unified Lyapunov functional for an age-structured model describing a virus infection. Our main contribution is to consider a very general nonlinear infection function, gathering almost all usual ones, for the following problem: where T(t), i(t, a) and V(t) are the populations of uninfected cells, infected cells with infection age a and free virus at time t respectively. The functions \(\delta (a),\) p(a), are respectively, the age-dependent per capita death, and the viral production rate of infected cells with age a. The global asymptotic analysis is established, among other results, by the use of compact attractor and strongly uniform persistence. Finally some numerical simulations illustrating our results are presented.
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$$\begin{aligned} \left\{ \begin{array}{lll} T'(t)=A- dT(t)-f(T(t),V(t)) \;\;\ t \ge 0,\\ i_t(t,a)+i_a(t,a)=-\delta (a) i(t,a), \\ V'(t)=\int _0^{\infty } p(a)i(t,a)da-cV(t), \end{array} \right. \end{aligned}$$
(0.1)
6.
We investigate a system of two nonlinear age-structured partial differential equations describing the dynamics of proliferating and quiescent hematopoietic stem cell (HSC) populations. The method of characteristics reduces the age-structured model to a system of coupled delay differential and renewal difference equations with continuous time and distributed delay. By constructing a Lyapunov–Krasovskii functional, we give a necessary and sufficient condition for the global asymptotic stability of the trivial steady state, which describes the population dying out. We also give sufficient conditions for the existence of unbounded solutions, which describe the uncontrolled proliferation of HSC population. This study may be helpful in understanding the behavior of hematopoietic cells in some hematological disorders. 相似文献
7.
Philippe Michel Tarik Mohamed Touaoula 《Mathematical Methods in the Applied Sciences》2013,36(3):323-335
In this paper, we consider nonlinear age‐structured equation with diffusion under nonlocal boundary condition and non‐negative initial data. More precisely, we prove that under some assumptions on the nonlinear term in a model of McKendrick–Von Foerster with diffusion in age, solutions exist and converge (long‐time convergence) towards a stationary solution. In the first part, we use classical analysis tools to prove the existence, uniqueness, and the positivity of the solution. In the second part, using comparison principle, we prove the convergence of this solution towards the stationary solution. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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