论文标题
具有分数laplacian和单数二次非线性的非线性PDE的爆炸
Blow-up for a nonlinear PDE with fractional Laplacian and singular quadratic nonlinearity
论文作者
论文摘要
我们考虑了一个抛物线型PDE，其扩散由分数拉普拉斯运算符和溶液“梯度”的二次非线性给出，并用单数项b响起。我们的第一个结果是解决这个问题的适当性：我们显示了（局部）轻度解决方案的存在和独特性。主要的结果是关于上述解决方案的爆炸，特别是我们在初始基准和术语B上找到足够的条件，以确保在有限的时间内爆炸解决方案。
We consider a parabolic-type PDE with a diffusion given by a fractional Laplacian operator and with a quadratic nonlinearity of the 'gradient' of the solution, convoluted with a singular term b. Our first result is the well-posedness for this problem: We show existence and uniqueness of a (local in time) mild solution. The main result is about blow-up of said solution, and in particular we find sufficient conditions on the initial datum and on the term b to ensure blow-up of the solution in finite time.
