Delayed diffusion with measure-valued kernels in nonlinear parabolic equations

2026/07/21 by Yuki Tsukamoto
#math.AP

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Abstract

We study nonlinear parabolic equations with delayed diffusion terms governed by finite signed measure kernels. The atom of the kernel at the origin is absorbed into the present-time operator, while the remaining part is treated as a residual delay kernel. Under structural assumptions on the effective present-time operators and a pathwise coercivity condition for the total memory operator, we prove the existence and uniqueness of weak solutions and their stability under weak-star convergence of the kernels. The stability result covers collapsing delayed atoms, whose mass is transferred to the present-time diffusion coefficient in the limit. We verify the assumptions for p-Laplacian type examples, including separated kernels and a regularized class of kernels reaching the origin.

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