Herrero, Miguel A.Velázquez, J.J. L.2023-06-202023-06-201996-090025-583110.1007/BF01445268https://hdl.handle.net/20.500.14352/57724The authors study a chemotactic model under certain assumptions and obtain the existence of a class of solutions which blow up at the center of an open disc in finite time. Such a finite-time blow-up of solutions implies chemotactic collapse, namely, concentration of species to form sporae. The model studied is the limiting case of a basic chemotactic model when diffusion of the chemical approaches infinity, which has the form ut=Δu−χ(uv), 0=Δv+(u−1), on ΩR2, where Ω is an open disc with no-flux (homogeneous Neumann) boundary conditions. The initial conditions are continuous functions u(x,0)=u0(x)≥0, v(x,0)=v0(x)≥0 for xΩ. Under these conditions, the authors prove there exists a radially symmetric solution u(r,t) which blows up at r=0, t=T<∞. A specific description of such a solution is presented. The authors also discuss the strong similarity between the chemotactic model they study and the classical Stefan problem.engjournal articlehttp://www.springerlink.com/content/k583061277m26u8x/http://www.springerlink.comrestricted access517.951:57Blow-upequationsradial solutionschemotactic collapseBiomatemáticasEcuaciones diferenciales2404 Biomatemáticas1202.07 Ecuaciones en Diferencias