BOUNDEDNESS AND BLOWUP SOLUTIONS FOR QUASILINEAR PARABOLIC SYSTEMS WITH LOWER ORDER TERMS

This paper deals with the bounded and blowup solutions of the quasilinear parabolic system u(t) = u(p) (Delta u + av) + f(u, v, Du, x) and v(t) = v(q) (Delta v + bu) + g(u, v, Dv, x) with homogeneous Dirichlet boundary condition. Under suitable conditions on the lower order terms f and g, it is shown that all solutions are bounded if (1 + c(1)) root ab < lambda(1) and blow up in a finite time if (1 + c(1)) root ab > lambda(1), where lambda(1) is the first eigenvalue of -Delta in Omega with Dirichlet data and c(1) > -1 related to f and g.