Oscillation of systems of quasilinear parabolic functional-differential equations about boundary value problems (Q2739189)

The authors are concerned with the oscillations of a system of quasilinear parabolic functional-differential equations NEWLINE\[NEWLINE\begin{multlined} \frac{\partial}{\partial t} \Biggl[u_i(x,t)-\sum_{k=1}^nc_k(t)u_i(x,t-\tau_k)\Biggr]= a_i(t)\Delta u_i(x,t)+\sum_{j=1}^ma_{ij}(t)\Delta u_j(x,\rho(t))-p_i(x,t)u_i(x,t)\\ -\sum_{j=1}^mf_{ij}[t,x,u_j(x,\sigma(t))],\qquad i=1,\dots,m,\quad (x,t)\in \Omega\times [0,\infty)\end{multlined}NEWLINE\]NEWLINE under Robin and Dirichlet boundary conditions: NEWLINE\[NEWLINE\frac{\partial u_i}{\partial\nu}+\psi_i(x,t)u_i=0, \quad (x,t)\in\partial\Omega\times [0,\infty),\;i=1,\dots,m,NEWLINE\]NEWLINE NEWLINE\[NEWLINEu_i(x,t)=0,\quad (x,t)\in\partial\Omega\times [0,\infty),\;i=1,\dots,m,NEWLINE\]NEWLINE where \(\Omega\subset \mathbb{R}^n\) is a bounded domain with piecewise smooth boundary. Sufficient conditions are obtained.