Asymptotic behavior for a time-dependent semilinear reaction–diffusion equation with a mixed local–nonlocal operator

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Abstract

In this paper, we consider a semilinear reaction–diffusion equation with a mixed local–nonlocal spatial operator and a time integral operator. The equation involves the mixed local–nonlocal Laplacian operator $\mathcal{L}=-\Delta+(-\Delta)^{\alpha / 2}$ and the Riemann–Liouville fractional integral operator $I_{0 \mid t}^{1-\gamma}$. Our main goal is to characterize the large–time asymptotic behavior of global mild solutions.

Keywords

global mild solution / anomalous diffusion / reaction–diffusion / mixed local–nonlocal Laplacian operator / nonlinear memory

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