Integral solution to a parabolic equation involving the fractional p-Laplacian operator - EL HATHOUT, Mohamed; FAHIM, Houda; ALAA, Nour Eddine (Studia Universitatis Babeș-Bolyai Mathematica, 2025)
The aim of this work is to study the existence and uniqueness of integral solutions for a class of non-local parabolic equations. There are two main results. First, we use a subdifferential technique to verify the existence and uniqueness of weak solutions when the initial data belong to L2. Secondly, the existence and uniqueness of an integral solution is demonstrated by extending the study to initial data in L1 space. To overcome the difficulties caused by non-local terms, the proposed strategy combines new approaches with sophisticated strategies derived from the theory of accretive operators. These results contribute to a better understanding of non-local evolution equations and their applications. Mathematics Subject Classification (2010): 34K37, 35C15, 35D30, 35A02. Received 29 May 2025; Accepted 20 July 2025.