Entropy solutions for time-fractional porous medium type equations

2023/02/13 by Kerstin Schmitz, Schmitz, Kerstin, Petra Wittbold +1 · 2 citations
Mathematics · Engineering · #Nonlinear Partial Differential Equations #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2302.06399

Abstract

In this paper we prove existence of entropy solutions to the time-fractional porous medium type equation, ∂_t[k∗(u-u₀)]-div (A(t,x)∇φ(u))=f in Q_T=(0,T)×Ω, with Dirichlet boundary condition, initial condition u(0,⋅)=u₀ in Ω, and L¹-data f∈ L¹((0,T)×Ω), u₀∈ L¹(Ω). To this end we approximate the data by L^∞-functions, use a known existence result of weak solutions for these more regular data, and additionally a known contraction principle for weak solutions, which can be adopted to the entropy solutions.

Cited by

• Duality estimates for subdiffusion problems including time-fractional porous medium type equations
• Global well-posedness for a time-fractional doubly nonlinear equation

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