共查询到20条相似文献,搜索用时 31 毫秒
1.
E. V. Chebotaryova 《Russian Mathematics (Iz VUZ)》2010,54(5):75-77
In this paper we apply the method of potentials for studying the Dirichlet and Neumann boundary-value problems for a B-elliptic equation in the form
$
\Delta _{x'} u + B_{x_{p - 1} } u + x_p^{ - \alpha } \frac{\partial }
{{\partial x_p }}\left( {x_p^\alpha \frac{{\partial u}}
{{\partial x_p }}} \right) = 0
$
\Delta _{x'} u + B_{x_{p - 1} } u + x_p^{ - \alpha } \frac{\partial }
{{\partial x_p }}\left( {x_p^\alpha \frac{{\partial u}}
{{\partial x_p }}} \right) = 0
相似文献
2.
ShuXing Chen 《中国科学A辑(英文版)》2009,52(9):1829-1843
In this paper we discuss the fundamental solution of the Keldysh type operator $
L_\alpha u \triangleq \frac{{\partial ^2 u}}
{{\partial x^2 }} + y\frac{{\partial ^2 u}}
{{\partial y^2 }} + \alpha \frac{{\partial u}}
{{\partial y}}
$
L_\alpha u \triangleq \frac{{\partial ^2 u}}
{{\partial x^2 }} + y\frac{{\partial ^2 u}}
{{\partial y^2 }} + \alpha \frac{{\partial u}}
{{\partial y}}
, which is a basic mixed type operator different from the Tricomi operator. The fundamental solution of the Keldysh type operator
with $
\alpha > - \frac{1}
{2}
$
\alpha > - \frac{1}
{2}
is obtained. It is shown that the fundamental solution for such an operator generally has stronger singularity than that
for the Tricomi operator. Particularly, the fundamental solution of the Keldysh type operator with $
\alpha < \frac{1}
{2}
$
\alpha < \frac{1}
{2}
has to be defined by using the finite part of divergent integrals in the theory of distributions. 相似文献
3.
Local and Global Existence of Solutions to Initial Value Problems of Nonlinear Kaup-Kupershmidt Equations 总被引:6,自引:0,他引:6
Shuang Ping TAO Shang Bin CUI 《数学学报(英文版)》2005,21(4):881-892
This paper is devoted to studying the initial value problems of the nonlinear Kaup Kupershmidt equations δu/δt + α1 uδ^2u/δx^2 + βδ^3u/δx^3 + γδ^5u/δx^5 = 0, (x,t)∈ E R^2, and δu/δt + α2 δu/δx δ^2u/δx^2 + βδ^3u/δx^3 + γδ^5u/δx^5 = 0, (x, t) ∈R^2. Several important Strichartz type estimates for the fundamental solution of the corresponding linear problem are established. Then we apply such estimates to prove the local and global existence of solutions for the initial value problems of the nonlinear Kaup- Kupershmidt equations. The results show that a local solution exists if the initial function u0(x) ∈ H^s(R), and s ≥ 5/4 for the first equation and s≥301/108 for the second equation. 相似文献
4.
Let f(n) be a strongly additive complex-valued arithmetic function. Under mild conditions on f, we prove the following weighted strong law of large numbers: if X,X
1,X
2, … is any sequence of integrable i.i.d. random variables, then
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