CRITICAL EXPONENT FOR A SYSTEM OF SLOW DIFFUSION EQUATIONS WITH BOTH REACTION AND ABSORPTION TERMS

摘要

Let Omega is a bounded domain in R-N with a smooth boundary partial derivative Omega, m, n > 1 and p, q, r, s, a, b are positive constants. For the initial and boundary value problem u(t) = Delta u(m) + v(p) - au(r), x is an element of Omega, t>0, v(t) = Delta v(n) + u(q) - bv(s), x is an element of Omega, t>0, u = v = 0, x is an element of partial derivative Omega, t>0, u(x, 0) = u(0)(x), v(x, 0) = v(0)(x), x is an element of Omega, we prove that all solutions are globally bounded if pq < max{n, r} max{n, s}; while there are finite time blowing up solutions if pq < max{n, r} max{n, s} and the initial data are sufficiently large. For the critical case pq = max{m, r} max{n, s}, the existence or nonexistence of global solutions depends on the relation between the exponents m, n, r, s, and also the range of the parameters a, b.