Existence of weak solutions for an abstract Cauchy problem involving the fractional Laplacian
Existence of weak solutions for an abstract Cauchy problem
Abstract
In this paper, we construct a theory of existence and uniqueness of solutions for an abstract Cauchy problem $ u'(t)+Au(t) = h(t)$, $t\in(0,T )$ and $u(0)=f$, where $A$ is the fractional Laplacian operator acting on a bounded domain with smooth boundary. The construction of the solution is based on the method of temporal discretization.
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Published
2026-03-21
Section
Research Articles
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