论文标题
在$ {\ mathbb r}^n $的半个半空间上的半线性热方程的初始迹线和可溶解度
Initial traces and solvability for a semilinear heat equation on a half space of ${\mathbb R}^N$
论文作者
论文摘要
我们在零dirichlet边界条件下，在$ {\ mathbb r}^n $的半空间上，非负解方程的非负解方程的初始痕迹的存在和独特性。此外，我们在初始数据上获得了必要的条件和足够条件，以解决相应的cauchy--dirichlet问题的解决性。我们的必要条件和足够的条件是鲜明的，使我们能够找到最佳的初始数据奇异性，以解决cauchy-dirichlet问题的解决性。
We show the existence and the uniqueness of initial traces of nonnegative solutions to a semilinear heat equation on a half space of ${\mathbb R}^N$ under the zero Dirichlet boundary condition. Furthermore, we obtain necessary conditions and sufficient conditions on the initial data for the solvability of the corresponding Cauchy--Dirichlet problem. Our necessary conditions and sufficient conditions are sharp and enable us to find optimal singularities of initial data for the solvability of the Cauchy--Dirichlet problem.
