(untitled) (Journal of Partial Differential Equations, 2019)
In this article, we study the system with boundary degeneracy u_it- rm div(a(x)| riangledown u_i|^p_i-2 abla u_i)=f_i(x,t,u_1,u_2), qquad (x,t) in Omega_T. Applying the monotone iterattion technique and the regularization method, we get the existence of solution for a regularized system. Moreover, under an integral condition on the coefficient function a(x), %00a0 And if00a0 % int_ Omega00a0 a(x)^- frac1min(p_1,p_2)-1 rm dx rm dt leq C , the existence and the uniqueness of the local solutions of the system is obtained by using a standard limiting process. Finally, the stability of the solutions is proved without any boundary value condition, provided a(x) satisfies another restriction."