Nonlinear stability of strong traveling waves for the singular Keller-Segel system with large perturbations
The authors study the nonlinear stability of traveling wave solutions for a system of parabolic equations in one space dimension \(u_t-\chi(uv)_x=Du_{xx}\), \(v_t+(\varepsilon v^2-u)_x=\varepsilon v_{xx}\), derived from a singular chemotaxis model describing the initiation of tumor angiogenesis. This paper provides a novel result on the asymptotic stability of large amplitude traveling waves with large initial perturbation for a system of conservation laws, although similar results have been available for some scalar equations. Extension of results to the initial data with lower regularity is also given.
scientific article; zbMATH DE number 6875586
scientific article