Asymptotic dynamics on a singular chemotaxis system modeling onset of tumor angiogenesis

The asymptotic behavior of solutions to a singular chemotaxis system modeling the onset of tumor angiogenesis in two and three dimensional whole spaces is investigated in the paper. By a Cole–Hopf type transformation, the singular chemotaxis is converted into a non-singular hyperbolic system. Then we study the transformed system and establish the global existence, asymptotic decay rates and diffusion convergence rate of solutions by the method of energy estimates. The main novelty of our results is the finding of a hidden interactive dissipation structure in the system by which the energy dissipation is established.