  This paper is concerned with the blowup phenomena for initial-boundary value
problem for certain semi linear parabolic, dispersive and hyperbolic equations
in cone-like domain. The result proposes a unified treatment of estimates for
lifespan of solutions to the problem by test function method. The Fujita
exponent p=1 + 2/N appears as a threshold of blowup phenomena for small data
when $C_{{\Sigma}}=R^N$ , but the case of cone-like domain with boundary the
threshold changes and explicitly given via the first eigenvalue of
corresponding Laplace-Beltrami operator with Dirichlet boundary condition as in
Levine-Meier in 1989.
