相对论性heat equation的最大值原理
Maximum principles for the relativistic heat equation
摘要：
经典热方程与相对论不相容，因为强最大值原理允许扰动瞬时传播。一些作者提出通过增加线性双曲线校正项来限制传播速度，但即使是弱最大值原理也不能成立。我们研究了一个最近引入的相对论热方程，它取代了拉普拉斯算子的拟线性椭圆算子，并表明，强和弱最大值原理分别为固定和随时间变化的解决方案，以及子和上解。此外，通过将方程转化为与中曲率算子相关的等价形式，我们证明了更强的相切和比较原理。
英文摘要：
The classical heat equation is incompatible with relativity, since the strong maximum principle allows for disturbances to propagate instantaneously. Some authors have proposed limiting the propagation speed by adding a linear hyperbolic correction term, but then even a weak maximum principle fails to hold. We study a more recently introduced relativistic heat equation, which replaces the Laplace operator by a quasilinear elliptic operator, and show that strong and weak maximum principles hold for stationary and time-varying solutions, respectively, as well as for sub- and supersolutions. Moreover, by transforming the equation into an equivalent form, related to the mean curvature operator, we prove even stronger tangency and comparison principles.
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