论文标题
分数扩散方程的非均匀初始边界值问题的弱和强溶液的适应性
Well-posedness for weak and strong solutions of non-homogeneous initial boundary value problems for fractional diffusion equations
论文作者
论文摘要
我们研究了与具有非雄源边界和初始值的时间分数扩散方程相关的初始边界值问题。我们认为解决问题的弱解决方案和强大解决方案。对于弱解决方案，我们引入了解决方案的新定义，该定义允许证明解决方案的初始边界值问题，具有非零的初始值和边界值，以及位于某些任意的负阶Sobolev空间中的非均匀术语。对于强大的解决方案，我们引入了最佳的兼容性条件，并证明了解决方案的存在。我们还引入了一些急剧的条件，以确保存在更规律性的解决方案的存在。
We study the well-posedness for initial boundary value problems associated with time fractional diffusion equations with non-homogenous boundary and initial values. We consider both weak and strong solutions for the problems. For weak solutions, we introduce a new definition of solutions which allows to prove the existence of solution to the initial boundary value problems with non-zero initial and boundary values and non-homogeneous terms lying in some arbitrary negative-order Sobolev spaces. For strong solutions, we introduce an optimal compatibility condition and prove the existence of the solutions. We introduce also some sharp conditions guaranteeing the existence of solutions with more regularity in time and space.
