共查询到20条相似文献,搜索用时 500 毫秒
1.
Terence Tao 《Journal of Differential Equations》2007,232(2):623-651
We show that the quartic generalised KdV equation
ut+uxxx+(u4x)=0 相似文献
2.
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
3.
In this paper, one-dimensional (1D) nonlinear Schrödinger equation
iut−uxx+mu+4|u|u=0 相似文献
4.
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
5.
In this paper we study the boundary behavior of solutions to equations of the form
∇⋅A(x,∇u)+B(x,∇u)=0, 相似文献
6.
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
7.
Ali Bentrad 《Journal of Differential Equations》2011,250(9):3652-3667
We give an explicit representation of the solutions of the Cauchy problem, in terms of series of hypergeometric functions, for the following class of partial differential equations with double characteristic at the origin:
(xkt∂+ax∂)(xkt∂+bx∂)u+cxk−1t∂u=0, 相似文献
8.
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
9.
Nguyen Huy Tuan Dang Duc Trong 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(7):1966-1972
The nonlinear backward Cauchy problem
ut+Au(t)=f(u(t)),u(T)=φ, 相似文献
10.
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
11.
R.F. Barostichi 《Journal of Differential Equations》2009,247(6):1899-260
Let (x,t)∈Rm×R and u∈C2(Rm×R). We study the Gevrey micro-regularity of solutions u of the nonlinear equation
ut=f(x,t,u,ux), 相似文献
12.
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
13.
Amin Esfahani 《Journal of Differential Equations》2009,247(12):3181-323
In this paper we study the generalized BO-ZK equation in two space dimensions
ut+upux+αHuxx+εuxyy=0. 相似文献
14.
15.
Bo Liang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(11):3815-3828
The paper first study the steady-state thin film type equation
∇⋅(un|∇Δu|q−2∇Δu)−δumΔu=f(x,u) 相似文献
16.
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
17.
18.
Tariel Kiguradze V. Lakshmikantham 《Journal of Mathematical Analysis and Applications》2006,324(2):1242-1261
For the nonlinear hyperbolic equation
u(2,1)=f(x,t,u,u(1,0),u(2,0),u(0,1),u(1,1)) 相似文献
19.
Let u be the weak solution to the degenerate Schrödinger equation with singular coefficients in Lipschitz domain as following
−div(w(x)A(x)∇u(x))+V(x)u(x)w(x)=0, 相似文献
20.
João Marcos do Ó Everaldo Medeiros 《Journal of Mathematical Analysis and Applications》2008,345(1):286-304
In this paper we study a class of nonhomogeneous Schrödinger equations
−Δu+V(x)u=f(u)+h(x) 相似文献