Regularity and existence for a mixed local-nonlocal parabolic equation with variable singularities and measure data

2025/09/05 by Das, Stuti
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.04797

Abstract

This article proves the existence, non-existence, regularity and asymptotic behavior of weak solutions for a class of mixed local-nonlocal parabolic problems involving singular nonlinearities and measure data extending the works of \citesanjitgarain,lazermc. A central contribution of this work is the inclusion of a variable singular exponent. We examine both the purely singular and perturbed singular cases in the context of measure-valued data, where the source terms can simultaneously take the form of measures. To the best of our knowledge, this phenomenon is new, even in the case of a constant singular exponent involving only a local operator. Further, all our results are also true for the operator being local only.

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Related

• Existence Theory for a class of semilinear mixed local and nonlocal equations involving variable singularities and singular measures
• On a mixed local-nonlocal evolution equation with singular nonlinearity
• On the regularity theory for mixed local and nonlocal quasilinear parabolic equations
• Gradient Hölder regularity in mixed local and nonlocal linear parabolic problem
• Combined effects in mixed local-nonlocal stationary problems