论文标题
$ \ mathbb {r}^n $中的进化分数p-laplacian方程。基本解决方案和渐近行为
The evolution fractional p-Laplacian equation in $\mathbb{R}^N$. Fundamental solution and asymptotic behaviour
论文作者
论文摘要
我们考虑自然依赖于时间的分数$ p $ -laplacian方程在整个欧几里得空间中带有参数$ p> 2 $和$ s \ in（0,1）$（分数指数）。我们表明，在Lebesgue $ l^Q $空间中的数据问题的库奇问题很好，并表明该解决方案构成了具有规律性和其他有趣属性的非表达半群的家族。作为主要结果，我们为每个质量价值$ m，$构建自相似的基本解决方案，并证明一般有限质量解决方案与在所有$ l^q $ spaces中具有相同质量的基本解决方案汇合。其他属性和估计数量完成了图片。
We consider the natural time-dependent fractional $p$-Laplacian equation posed in the whole Euclidean space, with parameters $p>2$ and $s\in (0,1)$ (fractional exponent). We show that the Cauchy Problem for data in the Lebesgue $L^q$ spaces is well posed, and show that the solutions form a family of non-expansive semigroups with regularity and other interesting properties. As main results, we construct the self-similar fundamental solution for every mass value $M,$ and prove that general finite-mass solutions converge towards that fundamental solution having the same mass in all $L^q$ spaces.A number of additional properties and estimates complete the picture.
