Results 21 to 30 of about 1,301 (120)
Open Mathematics, 2018 In this paper we investigate the stochastic retarded reaction-diffusion equations with multiplicative white noise on unbounded domain ℝn (n ≥ 2). We first transform the retarded reaction-diffusion equations into the deterministic reaction-diffusion ...
Jia Xiaoyao, Ding Xiaoquan, Gao Juanjuan
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Connections between the convective diffusion equation and the forced Burgers equation
International Journal of Stochastic Analysis, Volume 15, Issue 1, Page 53-69, 2002., 2002 The convective diffusion equation with drift b(x) and indefinite weight r(x), ∂ϕ∂t=∂∂x[a∂ϕ∂x−b(x)ϕ]+λr(x)ϕ, (1) is introduced as a model for population dispersal. Strong connections between Equation (1) and the forced Burgers equation with positive frequency (m ≥ 0), ∂u∂t=∂2u∂x2−u∂u∂x+mu+k(x), (2) are established through the Hopf‐Cole transformation ...
Nejib Smaoui, Fethi Belgacem
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Asymptotic behaviour of solutions for porous medium equation with periodic absorption
International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 1, Page 35-44, 2001., 2001 This paper is concerned with porous medium equation with periodic absorption. We are interested in the discussion of asymptotic behaviour of solutions of the first boundary value problem for the equation. In contrast to the equation without sources, we show that the solutions may not decay but may be “attracted” into any small neighborhood of the set ...
Yin Jingxue, Wang Yifu
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Advances in Nonlinear Analysis, 2019 This paper is concerned with the periodic traveling fronts for partially degenerate reaction-diffusion systems with bistable and time-periodic nonlinearity.
Wu Shi-Liang, Hsu Cheng-Hsiung
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On a comparison theorem for parabolic equations with nonlinear boundary conditions
Advances in Nonlinear Analysis, 2022 In this article, a new type of comparison theorem for some second-order nonlinear parabolic systems with nonlinear boundary conditions is given, which can cover classical linear boundary conditions, such as the homogeneous Dirichlet or Neumann boundary ...
Kita Kosuke, Ôtani Mitsuharu
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An inertial manifold and the principle of spatial averaging
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 5, Page 293-299, 2001., 2001 We examine the existence of inertial manifold of a class of differential equations with particular boundary conditions.
Hyukjin Kwean
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Local existence result of the single dopant diffusion including cluster reactions of high order
Abstract and Applied Analysis, Volume 6, Issue 1, Page 13-34, 2001., 2001 We consider the pair diffusion process which includes cluster reactions of high order. We are able to prove a local (in time) existence result in arbitrary space dimensions. The model includes a nonlinear system of reaction‐drift‐diffusion equations, a nonlinear system of ordinary differential equations in Banach spaces, and a nonlinear elliptic ...
R. Bader, W. Merz
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Large Time Behaviour of the Solution of a Nonlinear Diffusion Problem in Anthropology
Journal of Mathematical Study, 2018 In this article we consider a reaction-diffusion model for the spreading of farmers in Europe, which was occupied by hunter-gatherers; this process is known as the Neolithic agricultural revolution.
J. Eliaš
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Existence and regularity of pullback attractors for a non-autonomous diffusion equation with delay and nonlocal diffusion in time-dependent spaces [PDF]
arXiv, 2022 In this paper, we study the asymptotic behavior of solution to a non-autonomous diffusion equations with delay containing some hereditary characteristics and nonlocal diffusion in time-dependent space $C_{\mathcal{H}_{t}(\Omega)}$. When the nonlinear function $f$ satisfies the polynomial growth of arbitrary order $p-1$ $(p \ge 2)$ and the external ...
arxiv
Attractors of multivalued semiflows generated by differential inclusions and their approximations
Abstract and Applied Analysis, Volume 5, Issue 1, Page 33-46, 2000., 2000 We prove the existence of global compact attractors for differential inclusions and obtain some results concerning the continuity and upper semicontinuity of the attractors for approximating and perturbed inclusions. Applications are given to a model of regional economic growth.
Alexei V. Kapustian, José Valero
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