2018/03/06 by Francisco Guillén‐González, Guillén-González, F., María Ángeles Rodríguez‐Bellido +3 · 1 citation
Economics, Econometrics and Finance · Environmental Science · Mathematics · #35K51 #35Q92 #65M12 #65M15 #92C17 #Ecosystem dynamics and resilience #FOS: Mathematics #Mathematical Biology Tumor Growth #Numerical Analysis (math.NA) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1803.02386
openalex publication_date 2018/03/06 · openalex created_date 2018/03/29 · openalex updated_date 2026/07/28
We consider a chemo-repulsion model with quadratic production in a bounded domain. Firstly, we obtain global in time weak solutions, and give a regularity criterion (which is satisfied for 1D and 2D domains) to deduce uniqueness and global regularity. After, we study two cell-conservative and unconditionally energy-stable first-order time schemes: a (nonlinear and positive) Backward Euler scheme and a linearized coupled version, proving solvability, convergence towards weak solutions and error estimates. In particular, the linear scheme does not preserve positivity and the uniqueness of the nonlinear scheme is proved assuming small time step with respect to a strong norm of the discrete solution. This hypothesis is reduced to small time step in nD domains (n≤ 2) where global in time strong estimates are proved. Finally, we show the behavior of the schemes through some numerical simulations.