AI 中文总结
研究由有限符号测度核控制的带延迟扩散项的非线性抛物方程，通过有效当前算子结构假设和总记忆算子路径强制条件，证明弱解存在唯一性及稳定性，涵盖坍缩延迟原子，还验证了p - 拉普拉斯型例子假设。
AI 中文摘要
我们研究由有限符号测度核控制的带有延迟扩散项的非线性抛物方程。核在原点处的原子被吸收到当前算子中，其余部分视为残余延迟核。在有效当前算子的结构假设和总记忆算子的路径强制条件下，我们证明了弱解的存在唯一性及其在核的弱*收敛下的稳定性。稳定性结果涵盖坍缩延迟原子，其质量在极限情况下转移到当前扩散系数。我们验证了p - 拉普拉斯型例子的假设，包括分离核和一类到达原点的正则化核。
英文摘要
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.
Comments26 pages
