共查询到20条相似文献,搜索用时 0 毫秒
1.
Lu Yang 《Nonlinear Analysis: Real World Applications》2012,13(3):1069-1079
We consider the dynamical behavior of the reaction-diffusion equation with nonlinear boundary condition for both autonomous and non-autonomous cases. For the autonomous case, under the assumption that the internal nonlinear term f is dissipative and the boundary nonlinear term g is non-dissipative, the asymptotic regularity of solutions is proved. For the non-autonomous case, we obtain the existence of a compact uniform attractor in H1(Ω) with dissipative internal and boundary nonlinearities. 相似文献
2.
Takashi Narazaki 《Journal of Mathematical Analysis and Applications》2008,338(2):803-819
We consider the Cauchy problem for the damped wave equation
3.
Alexander Gladkov Tatiana Kavitova 《Mathematical Methods in the Applied Sciences》2020,43(8):5464-5479
We prove the global existence and blow-up of solutions of an initial boundary value problem for nonlinear nonlocal parabolic equation with nonlinear nonlocal boundary condition. Obtained results depend on the behavior of variable coefficients for large values of time. 相似文献
4.
Masakazu Yamamoto 《Journal of Mathematical Analysis and Applications》2010,369(1):144-163
We consider the large-time behavior of the solution to the initial value problem for the Nernst-Planck type drift-diffusion equation in whole spaces. In the Lp-framework, the global existence and the decay of the solution were shown. Moreover, the second-order asymptotic expansion of the solution as t→∞ was derived. We also deduce the higher-order asymptotic expansion of the solution. Especially, we discuss the contrast between the odd-dimensional case and the even-dimensional case. 相似文献
5.
Summary We give a complete classification of the small-amplitude finite-gap solutions of the sine-Gordon (SG) equation on an interval under Dirichlet or Neumann boundary conditions. Our classification is based on an analysis of the finite-gap solutions of the boundary problems for the SG equation by means of the Schottky uniformization approach.On leave from IPPI, Moscow, Russia 相似文献
6.
7.
Y. Xu 《Applicable analysis》2013,92(9):1143-1152
We consider a free boundary problem of heat equation with integral condition on the unknown free boundary. Results of solution regularity and problem well-posedness are presented. 相似文献
8.
Oscillation of a quasilinear impulsive delay parabolic equation with two different boundary conditions 总被引:1,自引:0,他引:1
In this paper, we discuss the oscillation for a class of quasilinear impulsive delay parabolic equations with two different boundary conditions and obtain several oscillation criteria. 相似文献
9.
Asymptotic simplification for a reaction-diffusion problem with a nonlinear boundary condition 总被引:2,自引:0,他引:2
de Pablo Arturo; Quiros Fernando; Rossi Julio D. 《IMA Journal of Applied Mathematics》2002,67(1):69-98
We study non-negative solutions of the porous medium equationwith a source and a nonlinear flux boundary condition, ut =(um)xx + up in (0, ), x (0, T); (um)x (0, t) = uq (0,t) for t (0, T); u (x, 0) = u0 (x) in (0, ), where m > 1,p, q > 0 are parameters. For every fixed m we prove thatthere are two critical curves in the (p, q-plane: (i) the criticalexistence curve, separating the region where every solutionis global from the region where there exist blowing-up solutions,and (ii) the Fujita curve, separating a region of parametersin which all solutions blow up from a region where both globalin time solutions and blowing-up solutions exist. In the caseof blow up we find the blow-up rates, the blow-up sets and theblow-up profiles, showing that there is a phenomenon of asymptoticsimplification. If 2q < p + m the asymptotics are governedby the source term. On the other hand, if 2q > p + m theevolution close to blow up is ruled by the boundary flux. If2q = p + m both terms are of the same order. 相似文献
10.
In this article we consider the inverse problem of identifying a time dependent unknown coefficient in a parabolic problem subject to initial and non-local boundary conditions along with an overspecified condition defined at a specific point in the spatial domain. Due to the non-local boundary condition, the system of linear equations resulting from the backward Euler approximation have a coefficient matrix that is a quasi-tridiagonal matrix. We consider an efficient method for solving the linear system and the predictor–corrector method for calculating the solution and updating the estimate of the unknown coefficient. Two model problems are solved to demonstrate the performance of the methods. 相似文献
11.
Alexander Gladkov Mohammed Guedda 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(13):4573-4580
In this paper we consider a semilinear parabolic equation ut=Δu−c(x,t)up for (x,t)∈Ω×(0,∞) with nonlinear and nonlocal boundary condition u∣∂Ω×(0,∞)=∫Ωk(x,y,t)uldy and nonnegative initial data where p>0 and l>0. We prove some global existence results. Criteria on this problem which determine whether the solutions blow up in finite time for large or for all nontrivial initial data are also given. 相似文献
12.
Layered stable equilibria of a reaction-diffusion equation with nonlinear Neumann boundary condition
Arnaldo Simal do Nascimento Renato José de Moura 《Journal of Mathematical Analysis and Applications》2008,347(1):123-135
In this work we investigate the existence and asymptotic profile of a family of layered stable stationary solutions to the scalar equation ut=ε2Δu+f(u) in a smooth bounded domain Ω⊂R3 under the boundary condition εν∂u=δεg(u). It is assumed that Ω has a cross-section which locally minimizes area and limε→0εlnδε=κ, with 0?κ<∞ and δε>1 when κ=0. The functions f and g are of bistable type and do not necessarily have the same zeros what makes the asymptotic geometric profile of the solutions on the boundary to be different from the one in the interior. 相似文献
13.
14.
We establish an extension result of existence and partial regularity for the nonzero Neumann initial-boundary value problem of the Landau-Lifshitz equation with nonpositive anisotropy constants in thre... 相似文献
15.
Alexander Gladkov Kwang Ik Kim 《Journal of Mathematical Analysis and Applications》2008,338(1):264-273
In this paper, we consider a semilinear heat equation ut=Δu+c(x,t)up for (x,t)∈Ω×(0,∞) with nonlinear and nonlocal boundary condition and nonnegative initial data where p>0 and l>0. We prove global existence theorem for max(p,l)?1. Some criteria on this problem which determine whether the solutions blow up in a finite time for sufficiently large or for all nontrivial initial data or the solutions exist for all time with sufficiently small or with any initial data are also given. 相似文献
16.
We consider the Laplace equation in ? d?1 × ?+ × (0,+∞) with a dynamical nonlinear boundary condition of order between 1 and 2. Namely, the boundary condition is a fractional differential inequality involving derivatives of noninteger order as well as a nonlinear source. Nonexistence results and necessary conditions are established for local and global existence. In particular, we show that the critical exponent depends only on the fractional derivative of the least order. 相似文献
17.
M. Loayza 《Journal of Differential Equations》2006,229(2):509-528
We study the existence, uniqueness and regularity of positive solutions of the parabolic equation ut−Δu=a(x)uq+b(x)up in a bounded domain and with Dirichlet's condition on the boundary. We consider here a∈Lα(Ω), b∈Lβ(Ω) and 0<q?1<p. The initial data u(0)=u0 is considered in the space Lr(Ω), r?1. In the main result (0<q<1), we assume a,b?0 a.e. in Ω and we assume that u0?γdΩ for some γ>0. We find a unique solution in the space . 相似文献
18.
Sabrine Gontara Syrine Masmoudi 《Journal of Mathematical Analysis and Applications》2010,369(2):719-934
Let Ω be a C1,1-bounded domain in Rn for n?2. In this paper, we are concerned with the asymptotic behavior of the unique positive classical solution to the singular boundary-value problem Δu+a(x)u−σ=0 in Ω, u|∂Ω=0, where σ?0, a is a nonnegative function in , 0<α<1 and there exists c>0 such that . Here λ?2, μk∈R, ω is a positive constant and δ(x)=dist(x,∂Ω). 相似文献
19.
Guy Bayada 《Journal of Mathematical Analysis and Applications》2003,282(1):212-231
The asymptotic behaviour of a Stokes flow with Tresca free boundary friction conditions when one dimension of the fluid domain tends to zero is studied. A specific Reynolds equation associated with variational inequalities is obtained and uniqueness is proved. 相似文献
20.
In this paper, we prove the relation v(t)?u(t,x)?w(t), where u(t,x) is the solution of an impulsive parabolic equations under Neumann boundary condition ∂u(t,x)/∂ν=0, and v(t) and w(t) are solutions of two impulsive ordinary equations. We also apply these estimates to investigate the asymptotic behavior of a model in the population dynamics, and it is shown that there exists a unique solution of the model which converges to the periodic solution of an impulsive ordinary equation asymptotically. 相似文献