Landis-type results for discrete equations
arxiv(2024)
摘要
We prove Landis-type results for both the semidiscrete heat and the
stationary discrete Schrödinger equations. For the semidiscrete heat equation
we show that, under the assumption of two-time spatial decay conditions on the
solution u, then necessarily u≡ 0. For the stationary discrete
Schrödinger equation we deduce that, under a vanishing condition at infinity
on the solution u, then u≡ 0. In order to obtain such results, we
demonstrate suitable quantitative upper and lower estimates for the L^2-norm
of the solution within a spatial lattice (hℤ)^d. These estimates
manifest an interpolation phenomenon between continuum and discrete scales,
showing that close-to-continuum and purely discrete regimes are different in
nature.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要