共查询到20条相似文献,搜索用时 9 毫秒
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This work is concerned with the fast diffusion equation
ut = ?·(um-1 ?u) (*) u_t = \nabla \cdot \big(u^{m-1} \nabla u\big) \qquad (\star) 相似文献
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The diffusive relaxation limit of non-isentropic Euler-Maxwell equations for plasmas 总被引:1,自引:0,他引:1
Jianwei Yang Shu Wang Dang Luo 《Journal of Mathematical Analysis and Applications》2011,380(1):343-353
This paper concerns the non-isentropic Euler-Maxwell equations for plasmas with short momentum relaxation time. With the help of the Maxwell-type iteration, it is obtained that, as the relaxation time tends to zero, periodic initial-value problem of certain scaled non-isentropic Euler-Maxwell equations has unique smooth solutions existing in the time interval where the corresponding classical drift-diffusion model has smooth solutions. Meanwhile, we justify a formal derivation of the corresponding drift-diffusion model from the non-isentropic Euler-Maxwell equations. 相似文献
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Razvan Gabriel Iagar Ariel Sánchez 《Journal of Mathematical Analysis and Applications》2009,351(2):635-652
In this paper we continue the study of the radial equivalence between the porous medium equation and the evolution p-Laplacian equation, begun in a previous work. We treat the cases m<0 and p<1. We perform an exhaustive study of self-similar solutions for both equations, based on a phase-plane analysis and the correspondences we discover. We also obtain special correspondence relations and self-maps for the limit case m=−1, p=0, which is particularly important in applications in image processing. We also find self-similar solutions for the very fast p-Laplacian equation that have finite mass and, in particular, some of them that conserve mass, while this phenomenon is not true for the very fast diffusion equation. 相似文献
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《Applied Mathematics Letters》2002,15(2):131-135
A stable relaxation approximation for a transport equation with the diffusive scaling is developed. The relaxation approximation leads in the small mean free path limit to the higher-order diffusion equation obtained from the asymptotic analysis of the transport equation. 相似文献
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Guy Bernard 《Mathematical Methods in the Applied Sciences》2000,23(11):965-984
A priori estimates are established for the very fast diffusion equation in \thispagestyle{empty}$\mathbb{R} \times (0,T)$ where in the form of necessary conditions on the initial value and the time level T. The demonstration is based on the volumetric mean of the solutions. Also, given are a priori estimates for the related elliptic equation in \thispagestyle{empty}$\mathbb{R}^n$ where and in the form of necessary conditions on the non‐homogeneous term ƒ(x) and the parameter λ. Necessary conditions on the domain of the evolution operator follows from these results. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
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Matteo Bonforte 《Advances in Mathematics》2010,223(2):529-578
We investigate qualitative properties of local solutions u(t,x)?0 to the fast diffusion equation, t∂u=Δ(um)/m with m<1, corresponding to general nonnegative initial data. Our main results are quantitative positivity and boundedness estimates for locally defined solutions in domains of the form [0,T]×Ω, with Ω⊆Rd. They combine into forms of new Harnack inequalities that are typical of fast diffusion equations. Such results are new for low m in the so-called very fast diffusion range, precisely for all m?mc=(d−2)/d. The boundedness statements are true even for m?0, while the positivity ones cannot be true in that range. 相似文献
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Abdelghani Bellouquid Nadia Chouhad 《Mathematical Methods in the Applied Sciences》2016,39(11):3136-3151
The paper is devoted to the study of the asymptotic behavior of the solutions of a kinetic model describing chemotaxis phenomena. Our interest focuses on the case, where the diffusion part dominates the chemotaxis part in the limit. More in detail, we prove that the solution of kinetic model exists globally and converges to a solution of diffusive limit. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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For any −1<m<0, positive functions f, g and u0≥0, we prove that under some mild conditions on f, g and u0 as R→∞ the solution uR of the Dirichlet problem ut=(um/m)xx in (−R,R)×(0,∞), u(R,t)=(f(t)|m|R)1/m, u(−R,t)=(g(t)|m|R)1/m for all t>0, u(x,0)=u0(x) in (−R,R), converges uniformly on every compact subset of R×(0,T) to the solution of the equation ut=(um/m)xx in R×(0,T), u(x,0)=u0(x) in R, which satisfies some mass loss formula on (0,T) where T is the maximal time such that the solution u is positive. We also prove that the solution constructed is equal to the solution constructed in Hui (2007) [15] using approximation by solutions of the corresponding Neumann problem in bounded cylindrical domains. 相似文献
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This article deals with the critical curve of a fast diffusive polytropic filtration system coupled at the boundary condition. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve. The critical curve of Fujita type is conjectured with the aid of some new results. 相似文献
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Jong Sheng Guo 《偏微分方程通讯》2013,38(9-10):1349-1365
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Masaaki Mizukami 《Mathematische Nachrichten》2018,291(8-9):1342-1355
This paper gives an insight into making a mathematical bridge between the parabolic‐parabolic signal‐dependent chemotaxis system and its parabolic‐elliptic version. To be more precise, this paper deals with convergence of a solution for the parabolic‐parabolic chemotaxis system with strong signal sensitivity to that for the parabolic‐elliptic chemotaxis system where Ω is a bounded domain in () with smooth boundary, is a constant and χ is a function generalizing In chemotaxis systems parabolic‐elliptic systems often gave some guide to methods and results for parabolic‐parabolic systems. However, the relation between parabolic‐elliptic systems and parabolic‐parabolic systems has not been studied except for the case that . Namely, in the case that Ω is a bounded domain, it still remains to analyze on the following question: Does a solution of the parabolic‐parabolic system converge to that of the parabolic‐elliptic system as ? This paper gives some positive answer in the chemotaxis system with strong signal sensitivity. 相似文献
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We present a generalization of Krylov-Rozovskii's result on the existence and uniqueness of solutions to monotone stochastic differential equations. As an application, the stochastic generalized porous media and fast diffusion equations are studied for σ-finite reference measures, where the drift term is given by a negative definite operator acting on a time-dependent function, which belongs to a large class of functions comparable with the so-called N-functions in the theory of Orlicz spaces. 相似文献
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Ph. Laurençot 《Annali di Matematica Pura ed Applicata》1998,175(1):233-251
We investigate the long-time behaviour of the solutions to the Cauchy problem
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This paper deals with the critical curve for a nonlinear boundary value problem of a fast diffusive non-Newtonian system. We first obtain the critical global existence curve by constructing the self-similar supersolution and subsolution. And then the critical Fujita curve is conjectured with the aid of some new results. 相似文献
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This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an -valued best bid price process and an -valued volume process. It is shown that under suitable assumptions the sequence of interpolated discrete time models is relatively compact in a localized sense and that any limit point satisfies a certain infinite dimensional SDE. Under additional assumptions on the dependence structure we construct two classes of models, which fit in the general framework, such that the limiting SDE admits a unique solution and thus the discrete dynamics converge to a diffusion limit in a localized sense. 相似文献
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Shu-Yu Hsu 《manuscripta mathematica》2013,140(3-4):441-460
Let n ≥ 3, 0 < m ≤ (n ? 2)/n, p > max(1, (1 ? m)n/2), and ${0 \le u_0 \in L_{loc}^p(\mathbb{R}^n)}$ satisfy ${{\rm lim \, inf}_{R\to\infty}R^{-n+\frac{2}{1-m}} \int_{|x|\le R}u_0\,dx = \infty}$ . We prove the existence of unique global classical solution of u t = Δu m , u > 0, in ${\mathbb{R}^n \times (0, \infty), u(x, 0) = u_0(x)}$ in ${\mathbb{R}^n}$ . If in addition 0 < m < (n ? 2)/n and u 0(x) ≈ A|x|?q as |x| → ∞ for some constants A > 0, q < n/p, we prove that there exist constants α, β, such that the function v(x, t) = t α u(t β x, t) converges uniformly on every compact subset of ${\mathbb{R}^n}$ to the self-similar solution ψ(x, 1) of the equation with ψ(x, 0) = A|x|?q as t → ∞. Note that when m = (n ? 2)/(n + 2), n ≥ 3, if ${g_{ij} = u^{\frac{4}{n+2}}\delta_{ij}}$ is a metric on ${\mathbb{R}^n}$ that evolves by the Yamabe flow ?g ij /?t = ?Rg ij with u(x, 0) = u 0(x) in ${\mathbb{R}^n}$ where R is the scalar curvature, then u(x, t) is a global solution of the above fast diffusion equation. 相似文献
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