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Laplacian Growth, Elliptic Growth, and Singularities of the Schwarz Potential
Laplacian Growth Elliptic Growth Singularities Schwarz Potential
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2010/12/13
The Schwarz function has played an elegant role in understanding and in generating new examples of exact solutions to the Laplacian growth (or \Hele-Shaw\) problem in the plane.
On Rayleigh-Type Formulas for a Non-local Boundary Value Problem Associated with an Integral Operator Commuting with the Laplacian
Rayleigh functions Laplacian eigenvalue problems non-local boundary conditions
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2010/12/9
In this article, we provide two different ways of producing recursive formulas for the Rayleigh functions of eigenvalues of the one-dimensional Laplacian with non-local boundary conditions, which comm...
Left-Inverses of Fractional Laplacian and Sparse Stochastic Processes
Left-Inverses of Fractional Laplacian Sparse Stochastic Processes
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2010/12/6
The fractional Laplacian (−△)/2 commutes with the primary coordination transformations in the Euclidean space Rd: dilation, translation and rotation.
IP-DGFEM method for the $p(x)$- Laplacian
free boundaries variable exponent spaces minimization
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2010/12/3
In this paper we construct an “Interior Penalty” Discontinuous Galerkin method to approximate the minimizer of a variational problem related to the p(x)−laplacian. The function p : ! [p1, p2] i...
Degenerate homogeneous parabolic equations associated with the infinity-Laplacian
Degenerate homogeneous parabolic equations infinity-Laplacian
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2010/12/8
We prove existence and uniqueness of viscosity solutions to the degenerate parabolic problem ut = h 1u where h 1 is the h-homogeneous operator associated with the infinity-Laplacian, h 1u = |Du|h&#...
The nodal line of the second eigenfunction of the Robin Laplacian in $\mathbb{R}^2$ can be closed
Laplacian eigenfunction nodal line Robin boundary
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2010/12/13
We construct a multiply connected domain in R2 for which the second eigenfunction of the Laplacian with Robin boundary condi-tions has an interior nodal line. In the process, we adapt a bound of Donne...
无穷区间上具有p-Laplacian算子的脉冲多点边值问题单调迭代正解的存在性
奇异脉冲方程 正解 迭代解 $p$-Laplacian
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2010/8/31
利用单调迭代方法得到了无穷区间上具有$p$-Laplacian算子的脉冲微分方程多点边值问题单调迭代正解的存在性, 同时也给出了解的相应迭代序列.
Triple positive solutions of four-point singular boundary value problems for p-Laplacian dynamic equations on time scales
Time scales Four-point singular boundary value problems
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2010/9/15
Let T be a time scale. We study the existence of three positive solutions for the nonlinear four-point singular boundary value problem with p-Laplacian operator on time scales. Some new results are ob...
Laplacian growth in the half plane
Laplacian growth half plane
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2010/4/7
We investigate a version of the Laplacian growth problem with zero surface tension in the half plane and find families of self-similar exact solutions.
无穷区间上具有pLaplacian算子的SturmLiouville型边值问题的迭代正解
奇异方程 迭代解 pLaplacian 无穷区间 一阶导数
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2009/12/23
利用单调迭代方法得到了无穷区间上具有pLaplacian算子的微分方程边值问题迭代正解的存在性, 同时 也得到了解的相应迭代序列。
一类pLaplacian多点边值问题单调迭代正解的存在性
pLaplacian 多点边值问题 单调迭代方法 锥
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2009/12/23
利用单调迭代方法获得了一类pLaplacian多点边值问题的正解迭代程序,这些迭代程序是从常值或者一次函数开始,是可行且有效的。文中还举了例子,进一步证实本文理论的严密性和可行性。
Lemniscates do not survive Laplacian growth
Lemniscates Laplacian growth
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2010/4/7
The large class of moving boundary processes in the plane modeled by the so-called Laplacian growth, which describes, e.g., solidification, electrodeposition, viscous fingering, bacterial growth, etc....
On some special solutions to periodic Benjamin-Ono equation with discrete Laplacian
Benjamin-Ono equation nonlocal integrable system Macdonald polynomial integrals of motion
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2010/4/8
We investigate a periodic version of the Benjamin-Ono (BO) equation associated with a discrete Laplacian. We find some special solutions to this equation, and calculate the values of the first two int...
高阶p-Laplacian算子方程组边值问题多个正解的存在性
p-Laplacian算子 高阶微分方程组 锥拉伸和锥压缩
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2009/11/25
应用锥拉伸和锥压缩不动点理论讨论了含p-Laplacian算子的高阶微分方程组边值问题多个正解的存在性.
具p-Laplacian非线性奇异边值系统正解的存在性
p-Laplacian算子 奇异边值系统 正解
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2009/11/19
研究了下面带有p-Laplacian算子的非线性奇异边值系统:(фp(u'i))'+ai(t)fi(u1,u2)=0, 0＜t＜1,αiфp(ui(0))-βiфp(u'i(0))=0, γiфp(ui(1))+δiфp(u'i(1))=0,(i=1,2)正解的存在性。其中фp(s)为p-Laplacian 算子，即фp(s)=|s|p-2s, p>1, (фp)-1=фq,1/p+1/q=1, ...