Existence of variational solutions to doubly nonlinear nonlocal evolution equations via minimizing movements

2022/01/03 by Suchandan Ghosh, Dharmendra Kumar, Ghosh, Suchandan +5
Computer Science · Mathematics · #35A01 #35A15 #35K51 #35R11 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2201.00634

openalex publication_date 2022/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove existence of variational solutions for a class of doubly nonlinear nonlocal evolution equations whose prototype is the double phase equation ∂_t u^m amp;+ P.V.∫_ℝ^N \frac|u(x,t)-u(y,t)|^p-2(u(x,t)-u(y,t))|x-y|^N+ps
amp;+a(x,y)\frac|u(x,t)-u(y,t)|^q-2(u(x,t)-u(y,t))|x-y|^N+qr dy = 0, mgt;0, pgt;1, s,r∈ (0,1). We make use of the approach of minimizing movements pioneered by DeGiorgi and Ambrosio and refined by B"ogelein, Duzaar, Marcellini, and co-authors to study nonlinear parabolic equations with non-standard growth.

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