Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary
Johannes Lankeit,
Michael Winkler
Abstract:The chemotaxis system u t = ∆u − ∇ • (u∇v), v t = ∆v − uv, is considered under the boundary conditions ∂u ∂ν − u ∂v ∂ν = 0 and v = v ⋆ on ∂Ω, where Ω ⊂ R n is a ball and v ⋆ is a given positive constant.In the setting of radially symmetric and suitably regular initial data, a result on global existence of bounded classical solutions is derived in the case n = 2, while global weak solutions are constructed when n ∈ {3, 4, 5}. This is achieved by analyzing an energy-type inequality reminiscent of global structur… Show more
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