The Global Existence And Nonexistence Of Solutions To Semilinear Parabolic Equations In R_+~N

This paper mainly studes the existence and nonexistence of global solutions to initial-boundary value problem of semilinear parabolic equations in R₊^N. The whole paper is consisted of the following three chapters.Chapter 1, introduces the background of the problem.Chapter 2, we mainly study the semilinear parabolic equationswhere p > 1, m, n, T > 0, x'∈R^N-1, x = (x',x_N), and u₀≥0 is a nonnegative continuous function in R₊^N.we obtain the following results:Theorem 1 If 1 < p < 1 + (?), then any solution of problem (1)blows up in finite time.Theorem 2 If p > 1+ (?), then problem (1)has global solution for small initial data u₀, while has no global solution for large data u₀ .Chapter 3, we mainly study the Non-homogeneous semilinear parabolic equationswhere p > 1, m, n, T > 0, u₀(x), f(x)≥0 and continuous in R₊^N. And we obtain the following results: Theorem 3 If 1 < p < 1 + (?), then any solution of (1)blows up in finite time.Theorem 4 If p > 1 + (?), then (2) has global solution for small initial data u₀ , while has no global solution for large data u₀ .