Well-posedness and regularity theory for the fractional diffusion-wave equation in Lebesgue spaces

2025/09/06 by Bruno de Andrade, de Andrade, Bruno, Santos, Naldisson
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2509.05654

openalex publication_date 2025/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is dedicated to the study of the semilinear fractional diffusion-wave equation. We provide estimates on the families of linear operators related to the problem in the fractional power scale associated with the Laplace operator. Furthermore, we analyze the existence and uniqueness of local mild solutions and their possible continuation to a maximal interval of existence. We also consider the issue of spatial regularity and continuous dependence with respect to initial data.

Citations

• Self-similar solutions for a superdiffusive heat equation with gradient nonlinearity
• On existence and uniqueness of solutions for semilinear fractional wave equations
• An L_q(L_p)-theory for the time fractional evolution equations with variable coefficients
• Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications

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