Long-time Behavior Of Solution For Reaction-diffusion Equation With Nonlinear Boundary Conditions

In this doctoral dissertation, we are mainly concerned with the long-time behaviors of solutions for the following two classes of reaction-diffusion equationswith nonlinear boundary condition and dynamical boundary condition:andIn abstract framework, based on the balance between the dissipative term f and the explosive term g (where the balance is given by the relationship between p+1 and 2q), we consider the reaction-diffusion equations with general nonlinearity of supercritical growth by using the concept of asymptotic a priori estimate.As applications to concrete problems, in Chapter 3 for the equation (Ⅰ), under the conditions that the interior and boundary nonlinear terms with supercritical growth satisfy the optimal balances (i.e., p+1> 2q), we establish the existence of attractors in space L^p+1(Ω). In Chapter 4, for the equation (Ⅱ) we prove the existence of attractors in product space L^p+1(Ω)×L^r+1(Γ), where the boundary nonlinearity is not a "good" term (i.e., the boundary term is no longer dissipative).