Existence of weak solutions for an abstract Cauchy problem involving the  fractional Laplacian: Existence of weak solutions for an abstract Cauchy problem

Ricardo Córdoba Gómez; Alex M.  Montes; Wilson E. Murillo

doi:10.5269/bspm.78417

Existence of weak solutions for an abstract Cauchy problem involving the fractional Laplacian

Existence of weak solutions for an abstract Cauchy problem

Authors

Ricardo Córdoba Gómez Universidad de NariÃ±o, Colombia
Alex M. Montes Universidad del Cauca
Wilson E. Murillo Universidad del Cauca

DOI:

https://doi.org/10.5269/bspm.78417

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.