On the oscillation of some impulsive parabolic equations with several delays. (Q2897391)

The authors investigate the parabolic delayed differential equation with several delays NEWLINE\[NEWLINE \frac {\partial }{\partial t}\biggl (u(t,x)- \sum _{j=1}^l b_j(t)u(\rho _j(t),x)\biggr ) - \sum _{i=1}^n a_i(t)\frac {\partial ^2u}{\partial x_i^2} (\tau (t),x) + \sum _{r=1}^m g_r(t,x)h_r\bigl (u(t-\eta _r,x)\bigr )= f(t,x),NEWLINE\]NEWLINE \(t\neq t_k \) with impulses at the points \(t_k\) of the form \(u({t_k}^+,x)-u({t_k}^-,x)=I\bigl (t_k,x,u(t_k,x)\bigr )\). Various conditions (rather technical) on the functions appearing in the investigated equation are given which guarantee that each solution of this equation oscillates.