Property Of Solutions For Semilinear Heat Equation With Inverse Potential

The blow-up theory of the solutions for nonlinear evolution equations is an important aspect of partial differential equation. In Chapter 2, we consider the properties of solitions for a semilinear heat equation u_t =Δu - V ( x )u + a ( x )u' pfor ( x , t )∈Ω×(0,∞) with nonlinear and nonlocal boundary condition u ( x , t ) =∫_ΩK ( x , y )u~l( y , t )dy onΩ×(0,∞). The conditions on the existence and nonexistence of global solutions are given by utilizing the method of subsolution and supersolution. In Chapter 3, we study the property of the equation with a gradient term and potential. We obtain the conditions for existence of solution by utilizing the regularity theory of parabolic equations and the approximate principle.