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 共查询到20条相似文献，搜索用时 406 毫秒
1.
The solvability of the nonlocal boundary value problem
in a class of functions is investigated for a quasilinear parabolic equation. The solution uniqueness follows from the maximum principle.  相似文献   

2.
We consider the first-order Cauchy problem
$ \begin{gathered} \partial _z u + a(z,x,D_x )u = 0,0 < z \leqslant Z, \hfill \\ u|_{z = 0} = u_0 , \hfill \\ \end{gathered} $ \begin{gathered} \partial _z u + a(z,x,D_x )u = 0,0 < z \leqslant Z, \hfill \\ u|_{z = 0} = u_0 , \hfill \\ \end{gathered}   相似文献   

3.
It is proved that the boundary-value problem
has a unique nonnegative solution if the following conditions are fulfilled:
. Bibliography: 2 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 215–222.  相似文献   

4.
The combinatorial identity
is established with the help of the differentiation of the convolution of some function with the sine function. Bibliography: 5 titles. __________ Translated from Problemy Matematicheskogo Analiza, No. 36, 2007, pp. 65–67.  相似文献   

5.
具时滞的奇异(n-1,1)共轭边值问题的多重正解   总被引：2，自引：0，他引：2  
Abstract. This paper discusses the singular (n-l, 1) conjugate boundary value problem as fol-lows by using a fixed point index theorem in cones  相似文献   

6.
Extensions of some inequalities   总被引：2，自引：0，他引：2  
Abstract. By using a simple analytic method the following inequalities are proved:  相似文献   

7.
Suppose a, b, and are reals witha<b and consider the following diffusion equation
  相似文献   

8.
We consider the three dimensional Cauchy problem for the Laplace equation uxx(x,y,z)+ uyy(x,y,z)+ uzz(x,y,z) = 0, x ∈ R,y ∈ R,0 z ≤ 1, u(x,y,0) = g(x,y), x ∈ R,y ∈ R, uz(x,y,0) = 0, x ∈ R,y ∈ R, where the data is given at z = 0 and a solution is sought in the region x,y ∈ R,0 z 1. The problem is ill-posed, the solution (if it exists) doesn't depend continuously on the initial data. Using Galerkin method and Meyer wavelets, we get the uniform stable wavelet approximate solution. Furthermore, we shall give a recipe for choosing the coarse level resolution.  相似文献   

9.
In this paper we consider a class of nonlinear elliptic problems of the type
$ \left\{ \begin{gathered} - div(a(x,\nabla u)) - div(\Phi (x,u)) = fin\Omega \hfill \\ u = 0on\partial \Omega , \hfill \\ \end{gathered} \right. $ \left\{ \begin{gathered} - div(a(x,\nabla u)) - div(\Phi (x,u)) = fin\Omega \hfill \\ u = 0on\partial \Omega , \hfill \\ \end{gathered} \right.   相似文献   

10.
The purpose of this paper is to study the existence of periodic solutions for the non-autonomous second order Hamiltonian system
$ \left\{ \begin{gathered} \ddot u(t) = \nabla F(t,u(t)),a.e.t \in [0,T], \hfill \\ u(0) - u(T) = \dot u(0) - \dot u(T) = 0 \hfill \\ \end{gathered} \right. $ \left\{ \begin{gathered} \ddot u(t) = \nabla F(t,u(t)),a.e.t \in [0,T], \hfill \\ u(0) - u(T) = \dot u(0) - \dot u(T) = 0 \hfill \\ \end{gathered} \right.   相似文献   

11.
In this paper we deal with the four-point singular boundary value problem
$ \left\{ \begin{gathered} (\phi _p (u'(t)))' + q(t)f(t,u(t),u'(t),u'(t)) = 0,t \in (0,1), \hfill \\ u'(0) - \alpha u(\xi ) = 0,u'(1) + \beta u(\eta ) = 0, \hfill \\ \end{gathered} \right. $ \left\{ \begin{gathered} (\phi _p (u'(t)))' + q(t)f(t,u(t),u'(t),u'(t)) = 0,t \in (0,1), \hfill \\ u'(0) - \alpha u(\xi ) = 0,u'(1) + \beta u(\eta ) = 0, \hfill \\ \end{gathered} \right.   相似文献   

12.
This paper concerns the study of the numerical approximation for the following initialboundary value problem
$ \left\{ \begin{gathered} u_t - u_{xx} = f\left( u \right), x \in \left( {0,1} \right), t \in \left( {0,T} \right), \hfill \\ u\left( {0,t} \right) = 0, u_x \left( {1,t} \right) = 0, t \in \left( {0,T} \right), \hfill \\ u\left( {x,0} \right) = u_0 \left( x \right), x \in \left[ {0,1} \right], \hfill \\ \end{gathered} \right. $ \left\{ \begin{gathered} u_t - u_{xx} = f\left( u \right), x \in \left( {0,1} \right), t \in \left( {0,T} \right), \hfill \\ u\left( {0,t} \right) = 0, u_x \left( {1,t} \right) = 0, t \in \left( {0,T} \right), \hfill \\ u\left( {x,0} \right) = u_0 \left( x \right), x \in \left[ {0,1} \right], \hfill \\ \end{gathered} \right.   相似文献   

13.
We discuss the existence of global classical solution for the uniformly parabolic equation
  相似文献   

14.
Ru Ying  XUE 《数学学报(英文版)》2010,26(12):2421-2442
we study an initial-boundary-value problem for the ＂good＂ Boussinesq equation on the half line
{δt^2u-δx^2u＋δx^4u＋δx^2u^2=0,t〉0,x〉0.
u（0,t）=h1（t）,δx^2u（0,t） =δth2（t）,
u（x,0）=f（x）,δtu（x,0）=δxh（x）.
The existence and uniqueness of low reguality solution to the initial-boundary-value problem is proved when the initial-boundary data （f, h, h1, h2） belong to the product space
H^5（R^＋）×H^s-1（R^＋）×H^s/2＋1/4（R^＋）×H^s/2＋1/4（R^＋）
1 The analyticity of the solution mapping between the initial-boundary-data and the with 0 ≤ s 〈 1/2. solution space is also considered.  相似文献   

15.
We study the existence of a solution to the nonlinear fourth-order elastic beam equation with nonhomogeneous boundary conditions
$\left\{ \begin{gathered} u^{(4)} (t) = f(t,u(t),u'(t),u'(t),u'(t)),a.e.t \in [0,1], \hfill \\ u(0) = a,u'(0) = b,u(1) = c,u'(1) = d, \hfill \\ \end{gathered} \right. $\left\{ \begin{gathered} u^{(4)} (t) = f(t,u(t),u'(t),u'(t),u'(t)),a.e.t \in [0,1], \hfill \\ u(0) = a,u'(0) = b,u(1) = c,u'(1) = d, \hfill \\ \end{gathered} \right.   相似文献   

16.
The existence of a positive solution for the generalized predator-prey model for two species
$ \begin{gathered} \Delta u + u(a + g(u,v)) = 0in\Omega , \hfill \\ \Delta v + v(d + h(u,v)) = 0in\Omega , \hfill \\ u = v = 0on\partial \Omega , \hfill \\ \end{gathered} $ \begin{gathered} \Delta u + u(a + g(u,v)) = 0in\Omega , \hfill \\ \Delta v + v(d + h(u,v)) = 0in\Omega , \hfill \\ u = v = 0on\partial \Omega , \hfill \\ \end{gathered}   相似文献   

17.
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18.
We study nonnegative solutions of the initial value problem for a weakly coupled system
  相似文献   

19.
We prove the existence and the uniqueness of a weak solution to the mixed boundary problem for the elliptic-parabolic equation
1, \hfill \\ \end{gathered} $$ " align="middle" vspace="20%" border="0">
with a monotone nondecreasing continuous function b. Such equations arise in the theory of non-Newtonian filtration as well as in the mathematical glaciology. Bibliography: 16 titles.  相似文献   

20.
The purpose of this paper is to obtain oscillation criteria for the differential system
  相似文献   

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