Integral solution to a parabolic equation involving the fractional p-Laplacian operator
DOI:
https://doi.org/10.24193/subbmath.2025.4.07Keywords:
fractional Laplacian, integral solutions, L^1 data, subdifferentialAbstract
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 \(L^2\). Secondly, the existence and uniqueness of an integral solution is demonstrated by extending the study to initial data in \(L^1\) 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. Non-local evolution equations and their applications are better understood thanks to these results.
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