Nonexistence for the Laplace equation with a dynamical boundary condition of fractional type

Mokhtar Kirane; Nasser-Eddine Tatar

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Nonexistence for the Laplace equation with a dynamical boundary condition of fractional type

机译：具有分数阶动力边界条件的Laplace方程的不存在

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摘要

We consider the Laplace equation in Rd-1 × R+ × (0,+∞) with a dynamical nonlinear boundary condition of order between 1 and 2. Namely, the boundary condition is a fractional differential inequality involving derivatives of noninteger order as well as a nonlinear source. Nonexistence results and necessary conditions are established for local and global existence. In particular, we show that the critical exponent depends only on the fractional derivative of the least order.

机译：我们考虑在Rd-1×R +×（0，+∞）的Laplace方程，其动态非线性边界条件的阶数在1和2之间。即，边界条件是一个分数阶微分不等式，涉及非整数阶导数以及一个非线性源。建立了不存在的结果和必要条件，以实现局部和全局存在。特别地，我们表明临界指数仅取决于最小阶的分数导数。

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《Siberian Mathematical Journal》 |2007年第5期|共8页
作者
Mokhtar Kirane; Nasser-Eddine Tatar;
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正文语种 eng
中图分类数学;
关键词
critical exponent; dynamical boundary condition; fractional derivative; Laplace equation;

机译：临界指数;动态边界条件;分数阶导数;拉普拉斯方程;

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1. Nonexistence for the Laplace equation with a dynamical boundary condition of fractional type [J] . Mokhtar Kirane, Nasser-Eddine Tatar Siberian Mathematical Journal . 2007,第5期

机译：具有分数阶动力边界条件的Laplace方程的不存在
2. Dynamics and stability of Hilfer-Hadamard type fractional pantograph equations with boundary conditions [J] . D. Vivek, K. Kanagarajan, S. Harikrishnan Journal of Nonlinear Analysis and Application . 2018,第1期

机译：具有边界条件的Hilfer-Hadamard型比例缩放弓方程的动力学和稳定性
3. Dynamics and stability of Hilfer-Hadamard type fractional differential equations with boundary conditions [J] . D. Vivek, K. Kanagarajan, S. Harikrishnan Journal of Nonlinear Analysis and Application . 2018,第1期

机译：具有边界条件的Hilfer-Hadamard型分数阶微分方程的动力学和稳定性
4. A numerical algorithm for solving Laplace and Poisson type partial differential equations on a uniform rectangular mesh with Dirichlet and Neumann boundary conditions [C] . Vasos Pavlika WSEAS International Conferences . 2008

机译：用Dirichlet和Neumann边界条件求解LAPLACH和泊松型偏微分方程的数值算法
5. Generalized Monotone Iterative Techniques for Fractional Differential Equations with Boundary Conditions. [D] . Ramirez-Valdez, Juan Diego. 2012

机译：带边界条件的分数阶微分方程的广义单调迭代技术。
6. Two generalized Lyapunov-type inequalities for a fractional p-Laplacian equation with fractional boundary conditions [O] . Yang Liu, Dapeng Xie, Dandan Yang, -1

机译：带分数边界条件的分数p-Laplacian方程的两个广义Lyapunov型不等式
7. Dynamics and stability of Hilfer-Hadamard type fractional pantograph equations with boundary conditions [O] . D. Vivek, K. Kanagarajan, S. Harikrishnan 2018

机译：具有边界条件的Hilfer-Hadamard型分数映射仪方程的动态与稳定性

Nonexistence for the Laplace equation with a dynamical boundary condition of fractional type

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