Uniform in time solutions for a chemotaxis with potential consumption model. (April 2023) - Corrêa Vianna Filho, André Luiz; Guillén-González, Francisco
Abstract: In this work we investigate the following chemo-attraction with consumption model in bounded domains of   R N ( N = 1, 2, 3 ): ∂ t u − Δ u = − ∇ ⋅ ( u ∇ v ), ∂ t v − Δ v = − u s v where s ≥ 1, endowed with isolated boundary conditions and initial conditions for ( u, v ) . The main novelty in the model is the nonlinear potential consumption term u s v . Through the convergence of solutions of an adequate truncated model, two main results are established; existence of uniform in time weak solutions in 3 D domains, and uniqueness and regularity in 2 D (or 1 D ) domains. Both results are proved imposing minimal regularity assumptions on the boundary of the domain.