## 2020年 7月 9日 (木) 16:30 開始

On the isoperimetric inequality and surface diffusion flow for multiply winding curves

## 2020年 7月 16日 (木) 16:30 開始

Md. Rabiul Haque 氏 (東北大学大学院理学研究科)

Critical Well-posedness of the Cauchy Problem to the Convection-Diffusion Equations in Uniformly Local Lebesgue Spaces

We consider the Cauchy problem of the convection-diffusion equations in uniformly local Lebesgue spaces. Uniformly local Lebesgue spaces is a space of functions which have the property that their elements have some uniform size when measured in balls of fixed radius but arbitrary center. Uniformly local Lebesgue spaces unlike the general Lebesguespaces, since the class of compact supported smooth functions is not dense, the heat semigroup cannot generate the $C_0$-semigroup. We construct the solution by the method of the integral equation via the heat semigroup in the case including the exponents before and after, in particular case of the critical exponent, the solution can be appropriately obtained even in the critical space.