论文标题
具有非线性边界条件的线性热方程的最佳liouville定理
An optimal Liouville theorem for the linear heat equation with a nonlinear boundary condition
论文作者
论文摘要
liouville定理用于整个空间和/或半空间中扩展不变的非线性抛物线问题（说该问题不具有始终定义的$ t \ in（ - \ infty，\ infty）$定义的正限制解决方案。我们证明了在半空间中线性方程的最佳liouville定理，并由非线性边界条件$ \ partial u/\partialν= u^q $，$ q> 1 $。
Liouville theorems for scaling invariant nonlinear parabolic problems in the whole space and/or the halfspace (saying that the problem does not posses positive bounded solutions defined for all times $t\in(-\infty,\infty)$) guarantee optimal estimates of solutions of related initial-boundary value problems in general domains. We prove an optimal Liouville theorem for the linear equation in the halfspace complemented by the nonlinear boundary condition $\partial u/\partialν=u^q$, $q>1$.
