Blow-Up Phenomena for Certain Nonlocal Evolution Equations and Systems

Abstract EN

We provide sufficient conditions for the nonexistence of global positive solutions to the nonlocal evolution equation utt(x,t)=(J ∗ u-u)(x,t)+up(x,t), (x,t)∈RN×(0,∞),(u(x,0),ut(x,0))=(u0(x),u1(x)), x∈RN, where J:RN→R+, p>1, and (u0,u1)∈Lloc1(RN;R+)×Lloc1(RN;R+).

Next, we deal with global nonexistence for certain nonlocal evolution systems.

Our method of proof is based on a duality argument.