共查询到20条相似文献，搜索用时 62 毫秒
1.
ＦＩＮＩＴＥＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＳＯＦＴＨＥＮＯＮＬＩＮＥＡＲＰＳＥＵＤＯ－ＰＡＲＡＢＯＬＩＣＳＹＳＴＥＭＤＵＭＩＮＧＳＨＥＮＧ（杜明笙）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＰｈｙｓｉｃｓａｎｄＣｏｍｐｕｔａｔｉｏｎａｌＭａｔｈｅｍａｔ... 相似文献
2.
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
3.
The article investigates the equation
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$ {u_t}{\text{ = }}{\left( {u{u_x}} \right)_x}{\text{ + }}\left( {u - {u_0}} \right)\left( {u - {u_1}} \right){\text{,}}\quad \quad {u_1} > {u_0} > 0. $ {u_t}{\text{ = }}{\left( {u{u_x}} \right)_x}{\text{ + }}\left( {u - {u_0}} \right)\left( {u - {u_1}} \right){\text{,}}\quad \quad {u_1} > {u_0} > 0. 相似文献
4.
We consider the following system of discrete equations . Criteria for the existence of three constant-sign solutions of the system will be developed. To illustrate the generality of the results obtained, we include applications to several well-known boundary value problems. Parallel results are also established for a system on {0,1,...} . 相似文献
5.
For the linear hyperbolic equations |
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6.
For quasilinear doubly degenerate parabolic equations it has been possible to establish the existence of nonnegative generalized solutions to the first boundary-value problem that are Hölder continuous up to the boundary of the cylinder Q T=Ωx(0, T]. A typical example of an admissible equation is the equation of Newtonian polytropic filtration $$\frac{{\partial u}}{{\partial t}} - \frac{\partial }{{\partial x_i }}\left\{ {a_0 \left| u \right|^l \left| {u_x } \right|^{m - 2} u_{x_i } } \right\} = 0, a_0 > 0,l > 0,m > 2.$$ . 相似文献
7.
ThisresearchissupportedbytheNationalNaturalScienceFoundationofChina.1.IntroductionInthispaper,weconsiderthefollowinginitial--boundaryvalueproblemwhereQ~fix(o,co),aQ=aflx(o,co),fiisaboundeddomaininEuclideanspaceR"(n22)withsmoothboundaryonandac=(u.,,'Iu..)denotesthegradientoffunctionu(x).Weassumethefunctionsal(x,t,u,p)(i=1,2,',n)anda(x,t,u,p)arelocallyH5ldercontinuousonfix(0,co)suchthatwherealtuandparepositiveconstants,m,aZIa3.hi,b2,alIadZ20,or321areconstants,m*E[0,m 2),hi16z/0,afl m*/… 相似文献
8.
The paper suggests some conditions on the lower order terms, which provide that the solution of the Dirichlet problem for
the general elliptic equation of the second order
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$
\begin{gathered}
- \sum\limits_{i,j = 1}^n {\left( {a_{i j} \left( x \right)u_{x_i } } \right)_{x_j } + } \sum\limits_{i = 1}^n {b_i \left( x \right)u_{x_i } - } \sum\limits_{i = 1}^n {\left( {c_i \left( x \right)u} \right)_{x_i } + d\left( x \right)u = f\left( x \right) - divF\left( x \right), x \in Q,} \hfill \\
\left. u \right|_{\partial Q} = u_0 \in L_2 \left( {\partial Q} \right) \hfill \\
\end{gathered}
$
\begin{gathered}
- \sum\limits_{i,j = 1}^n {\left( {a_{i j} \left( x \right)u_{x_i } } \right)_{x_j } + } \sum\limits_{i = 1}^n {b_i \left( x \right)u_{x_i } - } \sum\limits_{i = 1}^n {\left( {c_i \left( x \right)u} \right)_{x_i } + d\left( x \right)u = f\left( x \right) - divF\left( x \right), x \in Q,} \hfill \\
\left. u \right|_{\partial Q} = u_0 \in L_2 \left( {\partial Q} \right) \hfill \\
\end{gathered}
相似文献
9.
The initial value problems and the first boundary problems for the quasilinear wave equation $$u_{tt} - \left[ {a_0 + na_1 \left( {u_x } \right)^{n - 1} } \right]u_{xx} - a_2 u_{xxtt} = 0$$ are considered, where a 0, a 2 > 0 are constants, a 1 is an arbitrary real number, n is a natural number. The existence and uniqueness of the classical solutions for the initial value problems and the first boundary problems of the equation (1) are proved by the Galerkin method. 相似文献
10.
Consider the minimization problem in which
is a normal integrand. Define the convex function
by
It is known that, if the essential domain H of G is open, then problem (P) has a minimizer for any pair of endpoints ( u
0, u
1). In this paper, the same result is proved under the condition that, for every point p in H, the subgradient set G( p) is either bounded or empty (when H is open, this condition holds automatically). 相似文献
11.
This paper concerns the study of the numerical approximation for the following initialboundary value problem
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$
\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
12.
Conditions are given for the existence of solutions and the compactness of the set of solutions of the Darboux problem for the differential inclusion |
相似文献
13.
A new numerical inequality for average power means is presented. Let
and let
be a sequence of positive numbers. Consider the operator
. We denote by
the superposition of these operators. The following assertion is proved: if
. Bibliography: 2 titles. 相似文献
14.
This article concerns the boundary control on the side x = 0 when the other side x = l is fixed. The corresponding process of oscillations is studied for the time interval T > 0 and is described by the generalized solution of the equation This solution belongs to the class that admits the existence of finite energy for any time moment t. 相似文献
15.
The initial boundary value problem
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$ {*{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
16.
Suppose that is a trigonometric polynomial of the form ( z) = Nn=-N an zn. It is well-known that T is normal if and only if | a– N| = | aN| and the Fourier coefficients of satisfy the following symmetry condition:
In this paper we provide a complete criterion for hyponormality of T when satisfies a partial symmetry condition:
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17.
We discuss the existence of global classical solution for the uniformly parabolic equation
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18.
We shall consider the third order hyperbolic equation in [0, T] × Rx
where α ≥ 2, Β ≥ 1, η ≥ 0, λ ≥ 0, Σ ≥ 0, Μ ≥ 0, Ω ≥ 0 and θ ≥ 0 are integers. We prove that the Cauchy problem (1) is Gevrey well-posed. 相似文献
19.
In questo lavoro si considera il problema
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相似文献
20.
We study the asymptotic behavior as
of the Sobolev norm
of the solution to the Cauchy problem for the one-dimensional quasilinear Burgers type equation
(It is assumed that the problem is
, the boundary conditions are periodic, and
.) We show that the locally time-averaged Sobolev norms satisfy the estimate
. The estimates obtained as a consequence for the Fourier coefficients justify Kolmogorov's spectral theory of turbulence for the case of the Burgers equation. 相似文献
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