A note on comparison principle for p-laplacian evolution type equation

摘要

In this paper we provide a comparison principle for the weak solutions u(center dot,t),v(center dot,t) of two similar evolution p-Laplacian equations, both with source terms in a divergent and non-divergent form. Once we treat with signal solutions defined in all space Rn, for all t in a maximal existence interval [0,T*), the arguments presented here differ from the ones used to prove the comparison principle in bounded domains. We suppose p >= n and also consider some additional natural assumptions. The initial conditions u(center dot,0) and v(center dot,0) are supposed to belong to the space L1(Rn)boolean AND L infinity(Rn). An useful proposition to prove the comparison principle will be presented and the contraction of the L-1 norm of u-v for a particular case will be shown.