Existence and uniqueness for parabolic problems with Caputo time derivative

Abstract:

In this paper we are interested in the well-posedness of fully nonlinear Cauchy problems in which the time derivative is of Caputo type. We address this question in the framework of viscosity solutions, obtaining the existence via Perron's method, and comparison for bounded sub and supersolutions by a suitable regularization through inf and sup convolution in time. As an application, we prove the steady-state large time behavior in the case of proper nonlinearities and provide a rate of convergence by using the Mittag–Leffler operator.

Año de publicación:

2017

Keywords:

• Large time behavior
• Caputo derivative
• Nonlocal operator
• Comparison principle
• Viscosity solutions

Fuente:

scopus