共查询到20条相似文献,搜索用时 15 毫秒
1.
Quansen Jiu Tao PanDepartment of Mathematics Capital Normal University Beijing ChinaDepartment of Mathematics Information Science Guangxi University Nanning China Faculty of Bioresources Mie University Tsu Mie - Japan 《应用数学学报(英文版)》2003,19(2):297-306
Abstract This paper concerns the asymptotic behaviors of the solutions to the initial-boundary value prob-lem for scalar viscous conservations laws u_t+f(u)_x=u_(xx) on[0,1],with the boundary condition u(0,t) =u_,u(1,t)=u_+ and the initial data u(x,0)=u_0(x,0)=u_0(x),where u_≠u_+ and f is a given function satisfyingf'(u)>0 for u under consideration.By means of energy estimates method and under some more regular condi-tions on the initial data,both the global existence and the asymptotic behavior are obtained.When u_u_+, which corresponds to shock waves in inviscid conservation laws, it is established for weak shockwaves,which means that │u_-u_+│is small.Moreover,exponential decay rates are both given. 相似文献
2.
Mi-na Jiang~ Yan-ling Xu~ Laboratory of Nonlinear Analysis Department of Mathematics Central China Normal University Wuhan China Department of Information Computer Science College of Science Huazhong Agriculture University Wuhan China 《应用数学学报(英文版)》2005,21(1):31-42
We investigate the asymptotic behavior of solutions of the initial-boundary value problem for the generalized BBM-Burgers equation u_t f(u)_x=u_(xx) u_(xx) on the half line with the conditions u(0, t)=, u-, u(∞,t)=u_ and, u_-相似文献
3.
The authors study the p(x)-Laplacian equations with nonlinear boundary condition. By using the variational method, under appropriate assumptions on the perturbation terms f1 (x, u), f2(x, u) and h1(x), h2(x), such that the associated functional satisfies the "mountain pass lemma" and "fountain theorem" respectively, the existence and multiplicity of solutions are obtained. The discussion is based on the theory of variable exponent Lebesgue and Sobolev spaces. 相似文献
4.
Yakar Kannai 《Israel Journal of Mathematics》1990,71(3):349-351
The boundary value problemc
t=c
xx−c
yy+q(t,x)c with {fx349-1} was solved by Colton [1] forq analytic int. The solution may be used for mapping solutions of the heat equation into solutions ofu
t=u
xx+q(t,x)u. Solutions (of the boundary value problem) no longer exist ifq is not analytic int.
Erica and Ludwig Jesselson Professor of Theoretical Mathematics, The Weizmann Institute of Science. This research was partially
supported by the Minerva Foundation. 相似文献
5.
LiZhenayuan Taoliyuan YeQixiao 《高校应用数学学报(英文版)》1999,14(4):389-400
Abstract. In this paper, an initial boundary value problem with homogeneous Neumann bound-ary condition is studied for a reaction diffusion system which models the spread of infectious dis-eases within two population groups by means of serf and criss-cross infection mechanism, Exis-tence, uniqueness and houndedness of the nonnegative global solution 相似文献
6.
Three algorithms based on the bifurcation method are applied to solving the D4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bi- furcation parameter, the D4-Σd(D4-Σ1, D4-Σ2) symmetry-breaking bifurcation points on the branch of the D4 symmetric positive solutions are found via the extended systems. Finally, Σd(Σ1, Σ2) sym- metric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction. 相似文献
7.
Consider the Poisson's equation ψ" (x) = -ev-ψ eψ-v-N(x) with the Dirichlet boundary data, and we mainly investigate the inverse problem of determining the unknown function N(x) from a parameter function family. Some uniqueness and stability results in the inverse problem are obtained. 相似文献
8.
In this paper, we are concerned with the global singularity structures of weak solutions to 4-D semilinear dispersive wave
equations whose initial data are chosen to be discontinuous on the unit sphere. Combining Strichartz's inequality with the
commutator argument techniques, we show that the weak solutions are C2−regular away from the focusing cone surface |x|=|t−1| and the outgoing cone surface |x|=t+1.
This research was supported by the National Natural Science Foundation of China and the Doctoral Foundation of NEM of China. 相似文献
9.
10.
WANGXIANGRONG HANMAOAN 《高校应用数学学报(英文版)》1998,13(4):385-390
The authors consider the nonhnear systems x=h(y)-F(x),y=-g(x) in which g(x) may be not differentiabte and the system can be nonsymmetric. Some conditions which en-sure that there exists an infinite number of limit cycles are obtained. A problem about center-focus put forward by R. Conti has been answered. 相似文献
11.
WENGPEIXUAN 《高校应用数学学报(英文版)》1997,12(2):155-164
We use the topological degree method to deal with the generalized Sturm-Liouville boundary value problem (BVP) for second order mixed-type functional differential equation x(t)=f(t,xt,xt), 0≤t≤T. Existence principle and theorem for solutions of the BVP are obtained. 相似文献
12.
LetΔ_1(x;φ) be the error term of the first Riesz mean of the Rankin-Selberg problem. We study the higher power moments ofΔ_1(x;φ) and derive an asymptotic formula for the 3-rd, 4-th and 5-th power moments by using Ivic's large value arguments and other techniques. 相似文献
13.
Xiao-nlng Lin Hong Wang Da-qing Jiang 《应用数学学报(英文版)》2007,23(2):289-302
This paper is devoted to the study ofthe existence of single and multiple positive solutions forthe first order boundary value problem x′= f(t,x),x(0)=x(T),where f ∈ C([0,T]×R).In addition,weapply our existence theorems to a class of nonlinear periodic boundary value problems with a singularity at theorigin.Our proofs are based on a fixed point theorem in cones.Our results improve some recent results in theliteratures. 相似文献
14.
Lu Guofu 《高校应用数学学报(英文版)》1999,14(1):30-44
§1IntroductionInthepaper,weconsidertheinitialandboundaryvalueproblemasfolows:ut=Δ(gradφ(u))+αΔb(u)+f(x,t,u),(x,t)∈QT=Ω×(0,T](... 相似文献
15.
EXISTENCE AND UNIQUENESS FOR SECOND-ORDER VECTOR BOUNDARY VALUE PROBLEM OF NONLINEAR SYSTEMS 总被引:1,自引:0,他引:1
Du Zengji Lin Xiaojie Ge Weigao 《高校应用数学学报(英文版)》2005,20(3):323-330
This paper is concerned with the following second-order vector boundary value problem :x^R=f(t,Sx,x,x'),0〈t〈1,x(0)=A,g(x(1),x'(1))=B,where x,f,g,A and B are n-vectors. Under appropriate assumptions,existence and uniqueness of solutions are obtained by using upper and lower solutions method. 相似文献
16.
Yujuan Chen Mingxin Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2010,103(1):277-292
Under the proper structure conditions on the nonlinear term f(u) and weight function b(x), the paper shows the uniqueness and asymptotic behavior near the boundary of boundary blow-up solutions to the porous media
equations of logistic type −Δu = a(x)u
1/m
− b(x)f(u) with m > 1. 相似文献
17.
带非局部源的退化半线性抛物方程的解的爆破性质 总被引:1,自引:0,他引:1
This paper deals with the blow-up properties of the positive solutions to the nonlocal degenerate semilinear parabolic equation
u
t
− (x
a
u
x
)
x
=∫
0
a
f(u)dx in (0,a) × (0,T) under homogeneous Dirichlet conditions. The local existence and uniqueness of classical solution are established. Under
appropriate hypotheses, the global existence and blow-up in finite time of positve solutions are obtained. It is also proved
that the blow-up set is almost the whole domain. This differs from the local case. Furthermore, the blow-up rate is precisely
determined for the special case: f(u)=u
p
, p>1. 相似文献
18.
I. V. Filimonova 《Journal of Mathematical Sciences》2007,143(4):3415-3428
One considers a semilinear parabolic equation u
t
= Lu − a(x)f(u) or an elliptic equation u
tt
+ Lu − a(x)f(u) = 0 in a semi-infinite cylinder Ω × ℝ+ with the nonlinear boundary condition
, where L is a uniformly elliptic divergent operator in a bounded domain Ω ∈ ℝn; a(x) and b(x) are nonnegative measurable functions in Ω. One studies the asymptotic behavior of solutions of such boundary-value problems
for t → ∞.
__________
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 26, pp. 368–389, 2007. 相似文献
19.
O. A. Ladyzhenskaya 《Journal of Mathematical Sciences》1999,93(5):697-710
It is shown how to prove global unique solvability of the first initial-boundary value problem in the class of continuous
viscosity solutions for some classes of equations −ut+F(ux,uxx)=g(x, t, ux), where F(p, A) is elliptic only on some nonlinear subsets of values of the arguments (p, A). For this purpose we use the
techniques developed in the theory of viscosity solutions for degenerate elliptic equations. Bibliography: 12 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 233, 1996, pp. 112–130. 相似文献
20.
We present the bi-Hamiltonian structure and Lax pair of the equation ρt = bux+(1/2)[(u
2
−ux
2
)ρ]x, where ρ = u − uxx and b = const, which guarantees its integrability in the Lax pair sense. We study nonsmooth soliton solutions of this equation and show
that under the vanishing boundary condition u → 0 at the space and time infinities, the equation has both “W/M-shape” peaked soliton (peakon) and cusped soliton (cuspon) solutions. 相似文献