共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we study the existence, uniqueness and asymptotic stability of travelling wavefronts of the following equation:
ut(x,t)=D[u(x+1,t)+u(x-1,t)-2u(x,t)]-du(x,t)+b(u(x,t-r)), 相似文献
2.
We consider an Allen-Cahn type equation of the form ut=Δu+ε−2fε(x,t,u), where ε is a small parameter and fε(x,t,u)=f(u)−εgε(x,t,u) a bistable nonlinearity associated with a double-well potential whose well-depths can be slightly unbalanced. Given a rather general initial data u0 that is independent of ε, we perform a rigorous analysis of both the generation and the motion of interface. More precisely we show that the solution develops a steep transition layer within the time scale of order ε2|lnε|, and that the layer obeys the law of motion that coincides with the formal asymptotic limit within an error margin of order ε. This is an optimal estimate that has not been known before for solutions with general initial data, even in the case where gε≡0.Next we consider systems of reaction-diffusion equations of the form
3.
We study the convergence and decay rate to equilibrium of bounded solutions of the quasilinear parabolic equation
ut−diva(x,∇u)+f(x,u)=0 相似文献
4.
Markus Biegert 《Journal of Differential Equations》2009,247(7):1949-698
Let Ω⊂RN be a bounded domain and let μ be an admissible measure on ∂Ω. We show in the first part that if Ω has the H1-extension property, then a realization of the Laplace operator with generalized nonlinear Robin boundary conditions, formally given by on ∂Ω, generates a strongly continuous nonlinear submarkovian semigroup SB=(SB(t))t?0 on L2(Ω). We also obtain that this semigroup is ultracontractive in the sense that for every u,v∈Lp(Ω), p?2 and every t>0, one has
5.
Let M be a compact Riemannian manifold without boundary. Consider the porous media equation , u(0)=u0∈Lq, ? being the Laplace-Beltrami operator. Then, if q?2∨(m-1), the associated evolution is Lq-L∞ regularizing at any time t>0 and the bound ‖u(t)‖∞?C(u0)/tβ holds for t<1 for suitable explicit C(u0),γ. For large t it is shown that, for general initial data, u(t) approaches its time-independent mean with quantitative bounds on the rate of convergence. Similar bounds are valid when the manifold is not compact, but u(t) approaches u≡0 with different asymptotics. The case of manifolds with boundary and homogeneous Dirichlet, or Neumann, boundary conditions, is treated as well. The proof stems from a new connection between logarithmic Sobolev inequalities and the contractivity properties of the nonlinear evolutions considered, and is therefore applicable to a more abstract setting. 相似文献
6.
Yehuda Pinchover 《Journal of Functional Analysis》2004,206(1):191-209
In this paper we study the large time behavior of the (minimal) heat kernel kPM(x,y,t) of a general time-independent parabolic operator Lu=ut+P(x,∂x)u which is defined on a noncompact manifold M. More precisely, we prove that
7.
Steven D. Taliaferro 《Journal of Differential Equations》2011,250(2):892-928
We study classical nonnegative solutions u(x,t) of the semilinear parabolic inequalities
8.
M.R. Grossinho F.M. Minhós A.I. Santos 《Journal of Mathematical Analysis and Applications》2005,309(1):271-283
In this work we provide an existence and location result for the third-order nonlinear differential equation
u?(t)=f(t,u(t),u′(t),u″(t)), 相似文献
9.
We consider, for p∈(1,2) and q>1, self-similar singular solutions of the equation vt=div(|∇v|p−2∇v)−vq in Rn×(0,∞); here by self-similar we mean that v takes the form v(x,t)=t−αw(|x|t−αβ) for α=1/(q−1) and β=(q+1−p)/p, whereas singular means that v is non-negative, non-trivial, and for all x≠0. That is, we consider the ODE problem
(0.1) 相似文献
10.
Aubrey Truman 《Journal of Functional Analysis》2006,238(2):612-635
In this paper we study the initial problem for a stochastic nonlinear equation arising from 1D integro-differential scalar conservation laws. The equation is driven by Lévy space-time white noise in the following form:
(t∂−A)u+x∂q(u)=f(u)+g(u)Ft,x 相似文献
11.
We consider the blow-up of solutions of equations of the form
by means of a differential inequality technique. A lower bound for blow-up time is determined if blow-up does occur as well as a criterion for blow-up and conditions which ensure that blow-up cannot occur. 相似文献
ut=div(ρ(|∇u|2) grad u)+f(u)
12.
Jie Xiao 《Journal of Differential Equations》2006,224(2):277-295
Let u(t,x) be the solution of the heat equation (∂t-Δx)u(t,x)=0 on subject to u(0,x)=f(x) on Rn. The main goal of this paper is to characterize such a nonnegative measure μ on that f(x)?u(t2,x) induces a bounded embedding from the Sobolev space , p∈[1,n) into the Lebesgue space , q∈(0,∞). 相似文献
13.
Ki-ahm Lee 《Advances in Mathematics》2008,219(6):2006-2028
We consider the asymptotic profiles of the nonlinear parabolic flows ut=Δum to show the geometric properties of the following elliptic nonlinear eigenvalue problems:
14.
Linghai Zhang 《Journal of Differential Equations》2008,245(11):3470-3502
Let u=u(x,t,u0) represent the global strong/weak solutions of the Cauchy problems for the general n-dimensional incompressible Navier-Stokes equations
15.
16.
Zui-Cha Deng Liu Yang Guan-Wei Luo 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):6212-6221
This paper deals with the determination of a pair (p,u) in the nonlinear parabolic equation
ut−uxx+p(x)f(u)=0, 相似文献
17.
The reaction-diffusion delay differential equation
ut(x,t)−uxx(x,t)=g(x,u(x,t),u(x,t−τ)) 相似文献
18.
The aim of this paper is to discuss the Cauchy problem of the quasilinear hyperbolic equation of the form
ut+x(um)=up 相似文献
19.
We study the following complex Ginzburg-Landau equation with cubic nonlinearity on for under initial and Dirichlet boundary conditions u(x,0)=h(x) for x∈Ω, u(x,t)=Q(x,t) on ∂Ω where h,Q are given smooth functions. Under suitable conditions, we prove the existence of a global solution in H1. Further, this solution approaches to the solution of the NLS limit under identical initial and boundary data as a,b→0+. 相似文献
20.
In this paper a localized porous medium equation ut=ur(Δu+af(u(x0,t))) is considered. It is shown that under certain conditions solutions of the above equation blow up in finite time for large a or large initial data while there exist global positive solutions to the above equation for small a or small initial data. Moreover, it is also shown that all global positive solutions of the above equation are uniformly bounded, and this differs from that of a porous medium equation with a local source. 相似文献