具有非线性扩散的非局部聚集模型
On a nonlocal aggregation model with nonlinear diffusion
摘要：
考虑一类由生物聚集动力学研究而产生的具有非线性扩散的非局部聚集方程。作为退化抛物问题，我们证明了局部解的适定性、连续性准则和光滑性。对于紧支撑的非负光滑初值，我们证明了解的梯度在有限时间内发展为$L_x^\infty$ -范数爆破。
英文摘要：
We consider a nonlocal aggregation equation with nonlinear diffusion which arises from the study of biological aggregation dynamics. As a degenerate parabolic problem, we prove the well-posedness, continuation criteria and smoothness of local solutions. For compactly supported nonnegative smooth initial data we prove that the gradient of the solution develops $L_x^\infty$-norm blowup in finite time.
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