共查询到20条相似文献,搜索用时 170 毫秒
1.
带一类时滞项的生物种群扩散模型的行波解 总被引:1,自引:0,他引:1
本文利用Schauder不动点理论证明了微分积分方程组行波解u(x,t)=U(z),w(x,t)=W(z),z=xγ-ct的存在性.这个方程组描述了一类在植物上繁殖,且靠飞行在空中扩散的生物种群扩散过程.特别当时滞项,中积分核K(t)(反映种群繁殖模式)属于L1(0,∞)时,本文得到极限值W(-∞)(表示最终植物上种群密度)小于M.这个结论较符合生物实际. 相似文献
2.
Artur Sergyeyev 《Acta Appl Math》2010,109(1):273-281
We consider the Burgers-type system studied by Foursov,
${@{}rcl@{}}w_{t}&=&w_{xx}+8ww_{x}+(2-4\alpha)zz_{x},\\[6pt]z_{t}&=&(1-2\alpha)z_{xx}-4\alpha zw_{x}+(4-8\alpha)wz_{x}-(4+8\alpha)w^{2}z+(-2+4\alpha)z^{3},$\begin{array}{@{}rcl@{}}w_{t}&=&w_{xx}+8ww_{x}+(2-4\alpha)zz_{x},\\[6pt]z_{t}&=&(1-2\alpha)z_{xx}-4\alpha zw_{x}+(4-8\alpha)wz_{x}-(4+8\alpha)w^{2}z+(-2+4\alpha)z^{3},\end{array} 相似文献
3.
《复变函数与椭圆型方程》2012,57(10):881-889
In the present paper we have deduced the necessary and sufficient conditions on which an initial value problem $\fraca {\partial w}{\partial z_j} = a_j(z,\overline {z})\overline {w}+b_j(z,\overline {z})w+c_j(z,\overline {z}), \, j = 1,\ldots , n,\, w(z_0,\overline {z_0}) = w_0$ is locally solvable in the class of generalized analytic functions of several complex variables, which are functions fulfilling generalized Cauchy-Riemann System, $\fraca {\partial w}{\partial \overline {z_k}} = \overline {\alpha _k(z,\overline {z})}\, \overline {w}+ \overline {\beta _k(z,\overline {z})}w+ \overline {\gamma _k(z,\overline {z})},\, k = 1,\ldots , n$ . 相似文献
4.
Guoen HU 《数学年刊B辑(英文版)》2017,38(3):795-814
Let T_σ be the bilinear Fourier multiplier operator with associated multiplier σ satisfying the Sobolev regularity that sup κ∈Z∥σ_κ∥W~s(R~(2n)) ∞ for some s ∈ (n, 2n]. In this paper, it is proved that the commutator generated by T_σ and CMO(R~n) functions is a compact operator from L~(p1)(R~n, w_1) × L~(p2)(R~n, w_2) to L~p(R~n, ν_w) for appropriate indices p_1, p_2, p ∈ (1, ∞) with1 p=1/ p_1 +1/ p_2 and weights w_1, w_2 such that w = (w_1, w_2) ∈ A_(p/t)(R~(2n)). 相似文献
5.
Yao Biyun 《数学年刊B辑(英文版)》1982,3(1):85-88
Let $\sigma$ denote the family of univalent functions
$\[F(z) = z + \sum\limits_{n = 1}^\infty {\frac{{{b_n}}}{{{z^n}}}} \]$
in l< |z| <\infty if G(w) is the inverse of a function $F(z) \in \sigma ^'$, the expansion of G(w) in some neighborhood of w=\infty is
$\[G(w) = w - \sum\limits_{n = 1}^\infty {\frac{{{B_n}}}{{{w^n}}}} \]$
It is well known that |B_1|\leq 1 for any F(z) \in \sigma ^'. Springer^[1] proved that | B_3| \leq 1 and conjectured that
$\[|{B_{2n - 1}}| \le \frac{{(2n - 2)!}}{{n!(n - 1)!}}{\rm{ }}(n = 3,4, \cdots )\]$ (1)
Kubota^[2] proved (1) for n=3, 4, 5. Schober^[3] proved (1) for n = 6, 7. Ren Fuyao[4,5] has verified (1) for n=6, 7, 8. In this article we are going to verify (1) for n=9. 相似文献
6.
We study the reproducing kernel Hilbert spaces
with kernels of the form
7.
We characterize certain function classes in terms of the remainder in the quadrature formula \(\int_{ - \infty }^\infty {f(x)dx = (\pi /\sigma )\sum\nolimits_{v = - \infty }^\infty {f(v\pi /\sigma ) + R_\sigma [f]} } \) . In the process, we prove a generalization of the famous theorem of Paley and Wiener about entire functions of exponential type belonging toL 2 on the real line. 相似文献
8.
This paper deals with a two-competing-species chemotaxis system with two different chemicals 相似文献
$$\begin{aligned} \left \{ \textstyle\begin{array}{l@{\quad}l} \displaystyle u_{t}=\Delta u-\chi_{1}\nabla \cdot (u\nabla v)+\mu_{1} u(1-u-a _{1}w), & (x,t)\in \varOmega \times (0,\infty ), \\ \displaystyle \tau v_{t}=\Delta v-v+w, & (x,t)\in \varOmega \times (0,\infty ), \\ \displaystyle w_{t}=\Delta w-\chi_{2}\nabla \cdot (w\nabla z)+\mu_{2}w(1-a_{2}u-w), & (x,t)\in \varOmega \times (0,\infty ), \\ \displaystyle \tau z_{t}=\Delta z-z+u, & (x,t)\in \varOmega \times (0,\infty ), \end{array}\displaystyle \right . \end{aligned}$$ 9.
Kai WANG 《数学年刊B辑(英文版)》2007,28(3):321-326
Let M be an invariant subspace of Hv2. It is shown that for each f∈M⊥, f can be analytically extended across (?)Bd\σ(Sz1,…, Szd). 相似文献
10.
In this work, we prove the Cauchy–Kowalewski theorem for the initial-value problem 相似文献
$$\begin{aligned} \frac{\partial w}{\partial t}= & {} Lw \\ w(0,z)= & {} w_{0}(z) \end{aligned}$$ $$\begin{aligned} Lw:= & {} E_{0}(t,z)\frac{\partial }{\partial \overline{\phi }}\left( \frac{ d_{E}w}{dz}\right) +F_{0}(t,z)\overline{\left( \frac{\partial }{\partial \overline{\phi }}\left( \frac{d_{E}w}{dz}\right) \right) }+C_{0}(t,z)\frac{ d_{E}w}{dz} \\&+G_{0}(t,z)\overline{\left( \frac{d_{E}w}{dz}\right) } +A_{0}(t,z)w+B_{0}(t,z)\overline{w}+D_{0}(t,z) \end{aligned}$$ 11.
Let β 〉 0 and Sβ := {z ∈ C : |Imz| 〈β} be a strip in the complex plane. For an integer r ≥ 0, let H∞^Г,β denote those real-valued functions f on R, which are analytic in Sβ and satisfy the restriction |f^(r)(z)| ≤ 1, z ∈ Sβ. For σ 〉 0, denote by Bσ the class of functions f which have spectra in (-2πσ, 2πσ). And let Bσ^⊥ be the class of functions f which have no spectrum in (-2πσ, 2πσ). We prove an inequality of Bohr type
‖f‖∞≤π/√λ∧σ^r∑k=0^∞(-1)^k(r+1)/(2k+1)^rsinh((2k+1)2σβ),f∈H∞^r,β∩B1/σ, where λ∈(0,1),∧and ∧′are the complete elliptic integrals of the first kind for the moduli λ and λ′=√1- λ^2,respectively,and λ satisfies 4∧β/π∧′=1/σ. The constant in the above inequality is exact. 相似文献 12.
13.
Hu Ke 《数学年刊B辑(英文版)》1983,4(2):187-190
AIn this paper, the author obtains the following results:(1) If Taylor coeffiients of a function satisfy the conditions:(i),(ii),(iii)A_k=O(1/k) the for any h>0 the function φ(z)=exp{w(z)} satisfies the asymptotic equality the case h>1/2 was proved by Milin.(2) If f(z)=z α_2z~2 …∈S~* and,then for λ>1/2 相似文献
14.
Let Bσ,p,1 <-p<-∞, be the set of all functions from L8(R) which can be continued to entire functions of exponential type <-σ. The well known Shannon sampling theorem and its generalization [1] state that every f∈Bσ,p, 1<p<∞, can be represented as
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