On the existence of stationary solutions for certain systems of integro-differential equations with the double scale anomalous diffusion

2025/05/21 by Vitali Vougalter, Vitaly Volpert, Vougalter, Vitali +1
Mathematics · #35P30 #35R11 #45K05 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2505.15967

openalex publication_date 2025/05/21 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

The work deals with establishing the solvability of a system of integro-differential equations in the situation of the double scale anomalous diffusion. Each equation of such system involves the sum of the two negative Laplace operators raised to two distinct fractional powers in the space of three dimensions. The proof of the existence of solutions is based on a fixed point technique. We use the solvability conditions for the non-Fredholm elliptic operators in unbounded domains.

Citations

• A general theory for the (s, p)-superposition of nonlinear fractional operators
• An existence theory for nonlinear superposition operators of mixed fractional order
• An existence theory for superposition operators of mixed order subject to jumping nonlinearities
• Weak Error for Continuous Time Markov Chains Related to Fractional in Time P(I)DEs
• Solvability Conditions for Some non Fredholm Operators
• Anomalous transit-time dispersion in amorphous solids

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