共查询到20条相似文献,搜索用时 31 毫秒
1.
The paper deals with the radially symmetric solutions of ut=Δu+um(x,t)vn(0,t), vt=Δv+up(0,t)vq(x,t), subject to null Dirichlet boundary conditions. For the blow-up classical solutions, we propose the critical exponents for non-simultaneous blow-up by determining the complete and optimal classification for all the non-negative exponents: (i) There exist initial data such that u (v) blows up alone if and only if m>p+1 (q>n+1), which means that any blow-up is simultaneous if and only if m≤p+1, q≤n+1. (ii) Any blow-up is u (v) blowing up with v (u) remaining bounded if and only if m>p+1, q≤n+1 (m≤p+1, q>n+1). (iii) Both non-simultaneous and simultaneous blow-up may occur if and only if m>p+1, q>n+1. Moreover, we consider the blow-up rate and set estimates which were not obtained in the previously known work for the same model. 相似文献
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By a perturbation method and constructing comparison functions, we reveal how the inhomogeneous term h affects the exact asymptotic behaviour of solutions near the boundary to the problem △u=b(x)g(u)+λh(x), u>0 in Ω, u|∂Ω=∞, where Ω is a bounded domain with smooth boundary in RN, λ>0, g∈C1[0,∞) is increasing on [0,∞), g(0)=0, g′ is regularly varying at infinity with positive index ρ, the weight b, which is non-trivial and non-negative in Ω, may be vanishing on the boundary, and the inhomogeneous term h is non-negative in Ω and may be singular on the boundary. 相似文献
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In this paper, we study the regularity of generalized solutions u(x,t) for the n -dimensional quasi-linear parabolic diffraction problem. By using various estimates and Steklov average methods, we prove that (1): for almost all t the first derivatives ux(x,t) are Hölder continuous with respect to x up to the inner boundary, on which the coefficients of the equation are allowed to be discontinuous; and (2): the first derivative ut(x,t) is Hölder continuous with respect to (x,t) across the inner boundary. 相似文献
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Paul-Emile Maing 《Nonlinear Analysis: Theory, Methods & Applications》2008,68(12):3913-3922
This paper is concerned with the Cauchy problem for the fast diffusion equation ut−Δum=αup1 in RN (N≥1), where m∈(0,1), p1>1 and α>0. The initial condition u0 is assumed to be continuous, nonnegative and bounded. Using a technique of subsolutions, we set up sufficient conditions on the initial value u0 so that u(t,x) blows up in finite time, and we show how to get estimates on the profile of u(t,x) for small enough values of t>0. 相似文献
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We consider the semilinear parabolic equation ut=Δu+up on RN, where the power nonlinearity is subcritical. We first address the question of existence of entire solutions, that is, solutions defined for all x∈RN and t∈R. Our main result asserts that there are no positive radially symmetric bounded entire solutions. Then we consider radial solutions of the Cauchy problem. We show that if such a solution is global, that is, defined for all t?0, then it necessarily converges to 0, as t→∞, uniformly with respect to x∈RN. 相似文献
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We consider a multidimensional diffusion X with drift coefficient b(α,Xt) and diffusion coefficient ?σ(β,Xt). The diffusion sample path is discretely observed at times tk=kΔ for k=1…n on a fixed interval [0,T]. We study minimum contrast estimators derived from the Gaussian process approximating X for small ?. We obtain consistent and asymptotically normal estimators of α for fixed Δ and ?→0 and of (α,β) for Δ→0 and ?→0 without any condition linking ? and Δ. We compare the estimators obtained with various methods and for various magnitudes of Δ and ? based on simulation studies. Finally, we investigate the interest of using such methods in an epidemiological framework. 相似文献
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The initial boundary value problem for non-linear wave equations of Kirchhoff type with dissipation in a bounded domain is considered. We prove the blow-up of solutions for the strong dissipative term -Δut and the linear dissipative term ut by the energy method and give some estimates for the life span of solutions. We also show the nonexistence of global solutions with positive initial energy for non-linear dissipative term by Vitillaro's argument. 相似文献
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In this paper, we consider the problem (Pε) : Δ2u=un+4/n-4+εu,u>0 in Ω,u=Δu=0 on ∂Ω, where Ω is a bounded and smooth domain in Rn,n>8 and ε>0. We analyze the asymptotic behavior of solutions of (Pε) which are minimizing for the Sobolev inequality as ε→0 and we prove existence of solutions to (Pε) which blow up and concentrate around a critical point of the Robin's function. Finally, we show that for ε small, (Pε) has at least as many solutions as the Ljusternik–Schnirelman category of Ω. 相似文献
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The existence of solutions of degenerate quasilinear pseudoparabolic equations, where the term ∂tu is replace by ∂tb(u), with memory terms and quasilinear variational inequalities is shown. The existence of solutions of equations is proved under the assumption that the nonlinear function b is monotone and a gradient of a convex, continuously differentiable function. The uniqueness is proved for Lipschitz-continuous elliptic parts. The existence of solutions of quasilinear variational inequalities is proved under stronger assumptions, namely, the nonlinear function defining the elliptic part is assumed to be a gradient and the function b to be Lipschitz continuous. 相似文献
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The author deals with the quasilinear parabolic equation ut=[uα+g(u)]Δu+buα+1+f(u,∇u) with Dirichlet boundary conditions in a bounded domain Ω, where f and g are lower-order terms. He shows that, under suitable conditions on f and g, whether the solution is bounded or blows up in a finite time depends only on the first eigenvalue of −Δ in Ω with Dirichlet boundary condition. For some special cases, the result is sharp. 相似文献
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In this article, we consider a jump diffusion process (Xt)t≥0 observed at discrete times t=0,Δ,…,nΔ. The sampling interval Δ tends to 0 and nΔ tends to infinity. We assume that (Xt)t≥0 is ergodic, strictly stationary and exponentially β-mixing. We use a penalised least-square approach to compute two adaptive estimators of the drift function b. We provide bounds for the risks of the two estimators. 相似文献
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It is shown that if a sequence of open n-sets Dk increases to an open n-set D then reflected stable processes in Dk converge weakly to the reflected stable process in D for every starting point x in D. The same result holds for censored α-stable processes for every x in D if D and Dk satisfy the uniform Hardy inequality. Using the method in the proof of the above results, we also prove the weak convergence of reflected Brownian motions in unbounded domains. 相似文献
16.
In this paper, we establish an oscillation estimate of nonnegative harmonic functions for a pure-jump subordinate Brownian motion. The infinitesimal generator of such subordinate Brownian motion is an integro-differential operator. As an application, we give a probabilistic proof of the following form of relative Fatou theorem for such subordinate Brownian motion X in a bounded κ-fat open set; if u is a positive harmonic function with respect to X in a bounded κ-fat open set D and h is a positive harmonic function in D vanishing on Dc, then the non-tangential limit of u/h exists almost everywhere with respect to the Martin-representing measure of h. 相似文献
17.
Razvan Gabriel Iagar Juan Luis Vázquez 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009
We consider the Dirichlet problem for the p -Laplacian evolution equation, ut=Δpu, where p>2, posed in an exterior domain in RN, with zero Dirichlet boundary condition and with integrable and nonnegative initial data. We are interested in describing the influence of the holes of the domain on the large time behaviour of the solutions. Such behaviour varies depending on the relative values of N and p . We must distinguish between the behaviour near infinity of space (outer analysis), and near the holes (inner analysis). We obtain that the outer analysis is given in all cases by certain self-similar solutions and the inner analysis is given by quasi-stationary states. Logarithmic corrections to exact self-similarity appear in the critical case N=p, which is mathematically more interesting. In this first paper we treat only the cases N>p and N=p, the case N<p will be considered in a companion work. 相似文献
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A class of second-order abstract dissipative evolution differential operators D with 0∈kerD is shown for which the fact that a non-zero t?u(t) belongs to a cone and −Du to a dual cone may hold only on time intervals whose length is less than or equal to a defined number. Then oscillatory functions are dealt with in the framework of Banach spaces with a cone and conditions for the existence of a uniform oscillatory time for solutions of the equation Du=0 are given. 相似文献
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