On weakly coupled systems of partial differential equations with different diffusion terms

2021/12/30 by Davide Addona, Addona, Davide, Luca Lorenzi +1
Computer Science · Mathematics · #35B40 #35B65 #37L40 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary: 35K40 #Secondary: 35K45 #math.AP #msc:35B40 #msc:35B65 #msc:35K40 #msc:35K45 #msc:37L40

paper · pdf · doi:10.48550/arxiv.2112.14999

arxiv created 2021/12/30 · openalex publication_date 2021/12/30 · arxiv updated 2022/01/03 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We prove maximal Schauder regularity for solutions to elliptic systems and Cauchy problems, in the space C_b(ℝ^d;ℝ^m) of bounded and continuous functions, associated to a class of nonautonomous weakly coupled second-order elliptic operators \bf\mathcal A, with possibly unbounded coefficients and diffusion and drift terms which vary from equation to equation. We also provide estimates of the spatial derivatives up to the third-order and continuity properties both of the evolution operator \bf G(t,s) associated to the Cauchy problem D_t\bf u=\bf\mathcal A(t)\bf u in C_b(ℝ^d;ℝ^m), and, for fixed t, of the semigroup \bf T _t(τ) associated to the autonomous Cauchy problem D_τ\bf u=\bf\mathcal A( t)\bf u in C_b(ℝ^d;ℝ^m). These results allow us to deal with elliptic problems whose coefficients also depend on time.

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