论文标题
一个空间尺寸中完全非线性退化抛物线方程的能量公式
An energy formula for fully nonlinear degenerate parabolic equations in one spatial dimension
论文作者
论文摘要
能量（或Lyapunov）函数用于证明平衡的稳定性，或指示动态系统的梯度样结构。 Matano为准线性非降级抛物线方程构建了Lyapunov函数。我们修改了Matano的方法，以构建用于完全非线性退化抛物线方程的能量公式。我们提供了几个公式的例子，尤其是多孔培养基方程的新能量候选者。
Energy (or Lyapunov) functions are used to prove stability of equilibria, or to indicate a gradient-like structure of a dynamical system. Matano constructed a Lyapunov function for quasilinear non-degenerate parabolic equations. We modify Matano's method to construct an energy formula for fully nonlinear degenerate parabolic equations. We provide several examples of formulae, and in particular, a new energy candidate for the porous medium equation.
