Global and blow-up analysis for a class of nonlinear reaction diffusion model with Dirichlet boundary conditions

The work is concerned with the following nonlinear reaction diffusion model with Dirichlet boundary conditions: {(g(u))(t) = del center dot (rho vertical bar del u vertical bar(p-2) del u) + h(x)k(t)f(u), in D x (0, t*), u(x, t) = 0 on partial derivative D x (0, t*), u (x, 0) = u(0) (x) >= 0, in (D) over bar, where p >= 2 is a real number and D subset of R-N(N >= 2) is a bounded domain with smooth boundary partial derivative D. Under some appropriate assumptions on the functions f, h, k, g, rho, and initial value u(0), by defining auxiliary functions and using a first-order differential inequality technique, we not only present that the solution exists globally or blows up in a finite time but also compute the upper and lower bound for blow-up time when blow-up occurs. Additionally, two examples are given to illustrate the main results.