论文标题
描述肿瘤血管生成的非局部模型
A nonlocal model describing tumor angiogenesis
论文作者
论文摘要
在本文中，我们研究了血管生成的发作，并得出了一种描述它的新模型。该新模型采用具有扩散和分散术语的非本地汉堡方程式的形式。对于参数的特定值，方程将减少为$ \ partial_t p- \ frac {1} {2} {2}（ - δ） $ h $表示希尔伯变换。除了推导新模型外，我们还证明了许多适合的结果。最后，显示了一些初步数字。这些数字表明，方程的动力学足够丰富，可以在有限的时间内炸毁解决方案。
In this paper we study the onset of angiogenesis and derive a new model to describe it. This new model takes the form of a nonlocal Burgers equation with both diffusive and dispersive terms. For a particular value of the parameters, the equation reduces to $$ \partial_t p-\frac{1}{2}(-Δ)^{(α-1)/2}H \partial_t p=-\frac{1}{2}(-Δ)^{α/2} p+ p\partial_x p-\partial_x p, $$ where $H$ denotes the Hilber transform. In addition to the derivation of the new model, we also prove a number of well-posedness results. Finally, some preliminary numerics are shown. These numerics suggest that the dynamics of the equation is rich enough to have solutions that blow up in finite time.
