Heteroclinic connections for nonlocal equations
Heteroclinic connections for nonlocal equations
复制标题
非局部方程的异宿连接
DOI：
--
复制
发表时间：
2017
影响因子：
3.5
通讯作者：
E. Valdinoci
中科院分区：
文献类型：
--
作者：
S. Dipierro;S. Patrizi;E. Valdinoci
构造了一类强非局部积分微分方程的异宿轨。由于在这种强非局部状态下方程的能量是无穷大的，因此证明基于变分方法，依赖于重整化能量泛函，利用粘性型摄动方法，结合辅助罚函数法，发展了局部和非局部混合型双障碍问题的自由边界理论.由Peierls-Nabarro模型给出的扰动晶体中原子位错函数的定态位置的描述是所提出结果的一个特例。
We construct heteroclinic orbits for a strongly nonlocal integro-differential equation. Since the energy associated to the equation is infinite in such strongly nonlocal regime, the proof, based on variational methods, relies on a renormalized energy functional, exploits a perturbation method of viscosity type, combined with an auxiliary penalization method, and develops a free boundary theory for a double obstacle problem of mixed local and nonlocal type. The description of the stationary positions for the atom dislocation function in a perturbed crystal, as given by the Peierls–Nabarro model, is a particular case of the result presented.