共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
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
3.
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
4.
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
5.
Matteo Franca 《Journal of Differential Equations》2010,248(11):2629-2656
We consider the following equation
Δpu(x)+f(u,|x|)=0, 相似文献
6.
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
7.
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
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.
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
10.
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
11.
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
12.
13.
Vladislav V. Kravchenko Abdelhamid Meziani 《Journal of Mathematical Analysis and Applications》2011,377(1):420-427
We study the equation
−△u(x,y)+ν(x,y)u(x,y)=0 相似文献
14.
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
15.
We establish propagation and spreading properties for nonnegative solutions of nonhomogeneous reaction-diffusion equations of the type:
t∂u−∇⋅(A(t,x)∇u)+q(t,x)⋅∇u=f(t,x,u) 相似文献
16.
We study the stability of conservative solutions of the Cauchy problem for the Camassa-Holm equation ut−uxxt+κux+3uux−2uxuxx−uuxxx=0 with periodic initial data u0. In particular, we derive a new Lipschitz metric dD with the property that for two solutions u and v of the equation we have dD(u(t),v(t))?eCtdD(u0,v0). The relationship between this metric and usual norms in and is clarified. 相似文献
17.
Songzhe Lian Chunling Cao Hongjun Yuan 《Journal of Mathematical Analysis and Applications》2008,342(1):27-38
The authors of this paper study the Dirichlet problem of the following equation
ut−div(|u|ν(x,t)∇u)=f−|u|p(x,t)−1u. 相似文献
18.
Julián López-Gómez 《Journal of Differential Equations》2006,224(2):385-439
In this paper, we prove some optimal uniqueness results for large solutions of a canonical class of semilinear equations under minimal regularity conditions on the weight function in front of the non-linearity and combine these results with the localization method introduced in [López-Gómez, The boundary blow-up rate of large solutions, J. Differential Equations 195 (2003) 25-45] to prove that any large solution L of Δu=a(x)up, p>1, a>0, must satisfy
19.
In this paper we study the equation of viscoelasticity
utt−uxxt−Fx(ux)=f(x,t) 相似文献
20.
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