On a discrete scheme for time fractional fully nonlinear evolution equations

Article type: Research Article

Authors: Giga, Yoshikazu^a | Liu, Qing^b | Mitake, Hiroyoshi^{a; *}

Affiliations: [a] Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan. E-mails: labgiga@ms.u-tokyo.ac.jp, mitake@ms.u-tokyo.ac.jp | [b] Department of Applied Mathematics, Faculty of Science, Fukuoka University, Fukuoka 814-0180, Japan. E-mail: qingliu@fukuoka-u.ac.jp

Correspondence: [*] Corresponding author. E-mail: mitake@ms.u-tokyo.ac.jp.

Abstract: We introduce a discrete scheme for second order fully nonlinear parabolic PDEs with Caputo’s time fractional derivatives. We prove the convergence of the scheme in the framework of the theory of viscosity solutions. The discrete scheme can be viewed as a resolvent-type approximation.

Keywords: Approximation to solutions, Caputo’s time fractional derivatives, second order fully nonlinear equations, viscosity solutions

DOI: 10.3233/ASY-191583

Journal: Asymptotic Analysis, vol. 120, no. 1-2, pp. 151-162, 2020