On the local existence for a weakly parabolic system in Lebesgue spaces

Aparcana A.; Castillo R.; Guzmán-Rea O.; Loayza M. · Journal of Differential Equations (2020) · DOI: 10.1016/j.jde.2019.09.049

Resumen

We consider the parabolic system ut−aΔu=f(v),vt−bΔv=g(u) in Ω×(0,T), where a,b>0, f,g:[0,∞)→[0,∞) are non-decreasing continuous functions and either Ω is a bounded domain with smooth boundary ∂Ω or the whole space RN. We characterize the functions f and g so that the system has a local solution for every initial data (u0,v0)∈Lr(Ω)×Ls(Ω), u0,v0≥0, r,s∈[1,∞).

Instituciones: Universidad Nacional San Luis Gonzaga