Existence and uniqueness of weak solutions for nonlocal parabolic problems via the Galerkin method

Abstract:

Fractional differential equations are becoming increasingly popular as a modeling tool to describe a wide range of non-classical phenomena with spatial heterogeneities throughout the applied science and engineering. A recently developed nonlocal vector calculus is exploited to provide a variational analysis for a general class of nonlocal operators which include fractional Laplacians on bounded domains in Rn. We develop the Galerkin method to prove existence and uniqueness of weak solutions to nonlocal parabolic problems. Moreover, we study the existence of orthonormal basis of eigenvectors associated to these nonlocal operators.

Año de publicación:

2018

Keywords:

• Nonlocal operator
• Galerkin method
• weak solution
• Nonlocal vector calculus

Fuente:

scopus