A semilinear parabolic problem with variable reaction on a general domain

作者：Castillo Ricardo; Loayza Miguel^*

来源：Computers & Mathematics with Applications, 2017, 74(3): 351-359.

DOI：10.1016/j.camwa.2017.04.020

• Global existence
• Blow up
• Variable exponent

We are concerned with the parabolic equation u(t) - Delta u = f(t)u(p(x)) in Omega x (0, T) with homogeneous Dirichlet boundary condition, p is an element of C(Omega), f is an element of C(0, infinity)) and Omega is either a bounded or an unbounded domain. The initial data is considered in the space {u(0) is an element of C-0 (Omega); u(0) >= 0}. We find conditions that guarantee the global existence and the blow up in finite time of nonnegative solutions. These conditions are given in terms of the asymptotic behavior of the solution of the homogeneous linear problem u(t) - Delta u = 0.

• 出版日期2017-8-1