共查询到20条相似文献,搜索用时 46 毫秒
1.
The initial boundary value problem
$ {*{20}{c}} {\rho {u_{tt}} - {{\left( {\Gamma {u_x}} \right)}_x} + A{u_x} + Bu = 0,} \hfill & {x > 0,\quad 0 < t < T,} \hfill \\ {u\left| {_{t = 0}} \right. = {u_t}\left| {_{t = 0}} \right. = 0,} \hfill & {x \geq 0,} \hfill \\ {u\left| {_{x = 0}} \right. = f,} \hfill & {0 \leq t \leq T,} \hfill \\ $ \begin{array}{*{20}{c}} {\rho {u_{tt}} - {{\left( {\Gamma {u_x}} \right)}_x} + A{u_x} + Bu = 0,} \hfill & {x > 0,\quad 0 < t < T,} \hfill \\ {u\left| {_{t = 0}} \right. = {u_t}\left| {_{t = 0}} \right. = 0,} \hfill & {x \geq 0,} \hfill \\ {u\left| {_{x = 0}} \right. = f,} \hfill & {0 \leq t \leq T,} \hfill \\ \end{array} 相似文献
2.
W. G. Nowak 《Acta Mathematica Hungarica》2008,120(1-2):179-192
This article provides an asymptotic formula for the number of integer points in the three-dimensional body $$ \left( \begin{gathered} x \hfill \\ y \hfill \\ z \hfill \\ \end{gathered} \right) = t\left( \begin{gathered} (a + r\cos \alpha )\cos \beta \hfill \\ (a + r\cos \alpha )\sin \beta \hfill \\ r\sin \alpha \hfill \\ \end{gathered} \right),0 \leqq \alpha ,\beta < 2\pi ,0 \leqq r \leqq b, $$ for fixed a > b > 0 and large t. 相似文献
3.
Gao Feng Zheng 《数学学报(英文版)》2012,28(7):1491-1506
It is shown that any solution to the semilinear problem{ ut = uxx + δ(1-u)-p , (x, t) ∈ (-1 , 1) × (0 , T ), u( ±1 , t) = 0, t ∈ (0 , T ), u(x, 0) = u0(x) 1, x ∈ [ 1 , 1] either touches 1 in finite time or converges smoothly to a steady state as t →∞. Some extensions of this result to higher dimensions are also discussed. 相似文献
4.
Zhong-yuan LIU 《应用数学学报(英文版)》2013,29(2):415-424
Let BR be the ball centered at the origin with radius R in RN ( N ≥2). In this paper we study the existence of solution for the following elliptic systemu -△u+λu=p/(p + q)κ(| x |)) u(p-1)vq1,x ∈BR1,-△u+λu=p/(p + q)κ(| x |)) upv(q-1)1,x ∈BR1,u > 01,v > 01,x ∈ BR1,(u)/(v)=01,(v)/(v)=01,x ∈BRwhereλ > 0 , μ > 0 p ≥ 2, q ≥ 2,ν is the unit outward normal at the boundary BR . Under certainassumptions on κ ( | x | ), using variational methods, we prove the existence of a positive and radially increasing solution for this problem without growth conditions on the nonlinearity. 相似文献
5.
Ratikanta Panda 《Proceedings Mathematical Sciences》1995,105(4):425-444
Suppose Δn u = div (¦ ?u ¦n-2?u) denotes then-Laplacian. We prove the existence of a nontrivial solution for the problem $$\left\{ \begin{gathered} - \Delta _n u + \left| u \right|^{n - 2} u = \int {(x,u)u^{n - 2} in \mathbb{R}^n } \hfill \\ u \in W^{1,n} (\mathbb{R}^n ) \hfill \\ \end{gathered} \right.$$ wheref(x, t) =o(t) ast → 0 and ¦f(x, t)¦ ≤C exp(αn¦t¦n/(n-1)) for some constantC > 0 and for allx∈?;t∈? with αn =nω n 1/(n-1) , ωn = surface measure ofS n-1. 相似文献
6.
More work is done to study the explicit, weak and strong implicit difference solution for the first boundary problem of quasilinear parabolic system: $$\begin{gathered} u_t = ( - 1)^{M + 1} A(x,t,u, \cdots ,u_x M - 1)u_x 2M + f(x,t,u, \cdots u_x 2M - 1), \hfill \\ (x,t) \in Q_T = \left| {0< x< l,0< t \leqslant T} \right|, \hfill \\ u_x ^k (0,t) = u_x ^k (l,t) = 0 (k = 0,1, \cdots ,M - 1),0< t \leqslant T, \hfill \\ u(x,0) = \varphi (x),0 \leqslant x \leqslant l, \hfill \\ \end{gathered} $$ whereu, ?, andf arem-dimensional vector valued functions, A is anm×m positively definite matrix, and $u_t = \frac{{\partial u}}{{\partial t}},u_x ^k = \frac{{\partial ^k u}}{{\partial x^k }}$ . For this problem, the convergence of iteration for the general difference schemes is proved. 相似文献
7.
The paper is devoted to the study of the behavior of the following mixed problem for large values of time:
8.
The paper treats of the numerical approximation for the following boundary value problem: $$ \left\{ \begin{gathered} u_t (x,t) - u_{xx} (x,t) = 0, 0 < x < 1, t \in (0,T), \hfill \\ u(0,t) = 1, u_x (1,t) = - u^{ - p} (1,t), t \in (0,T), \hfill \\ u(x,0) = u_0 (x) > 0, 0 \leqslant x \leqslant 1, \hfill \\ \end{gathered} \right. $$ where p > 0, u 0 ∈ C 2([0, 1]), u 0(0) = 1, and u′ 0(1) = ?u 0 ?p (1). Conditions are specified under which the solution of a discrete form of the above problem quenches in a finite time, and we estimate its numerical quenching time. It is also proved that the numerical quenching time converges to real time as the mesh size goes to zero. Finally, numerical experiments are presented which illustrate our analysis. 相似文献
9.
In this paper, we deal with the oscillatory behavior of solutions of the neutral partial differential equation of the form $$\begin{gathered} \frac{\partial }{{\partial t}}\left[ {p\left( t \right)\frac{\partial }{{\partial t}}(u\left( {x,t} \right) + \sum\limits_{i = 1}^t {p_i \left( t \right)u\left( {x,t - \tau _i } \right)} )} \right] + q\left( {x,t} \right)f_j (u(x,\sigma _j (t))) \hfill \\ = a\left( t \right)\Delta u\left( {x,t} \right) + \sum\limits_{k = 1}^n {a_k \left( t \right)} \Delta u\left( {x,\rho _k \left( t \right)} \right), \left( {x,t} \right) \in \Omega \times R_ + \equiv G \hfill \\ \end{gathered} $$ where Δ is the Laplacian in EuclideanN-spaceR N, R+=(0, ∞) and Ω is a bounded domain inR N with a piecewise smooth boundary δΩ. 相似文献
10.
The modified Bernstein-Durrmeyer operators discussed in this paper are given byM_nf≡M_n(f,x)=(n+2)P_(n,k)∫_0~1p_n+1.k(t)f(t)dt,whereWe will show,for 0<α<1 and 1≤p≤∞ 相似文献
11.
This paper concerns the study of the numerical approximation for the following initialboundary value problem
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