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On a class of semilinear nonclassical fractional wave equations with logarithmic nonlinearity
Author(s) -
Vo Van Au,
Thi Kim Van Ho,
Nguyen Anh Tuan
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7466
Subject(s) - mathematics , uniqueness , sobolev space , logarithm , fractional calculus , nonlinear system , class (philosophy) , mathematical analysis , boundary value problem , embedding , fixed point theorem , interval (graph theory) , initial value problem , pure mathematics , combinatorics , physics , quantum mechanics , artificial intelligence , computer science
In this paper, we consider the initial boundary value problem for time‐fractional subdiffusive equations with Caputo derivative. Our problem has many applications in population dynamics. The source function is given in the logarithmic form. We examine the existence, uniqueness of local solutions, and their ability to continue to a maximal interval of existence. The main tool and analysis here are of applying some Sobolev embedding and some fixed point theorems.