The Blow-up Properties Of Solutions To Nonlinear Degenerate And Singular Parabolic Equations With Weighted Nonlocal Boundary Conditions

The blow-up of properties of the solution of the second order parabolic partial di?erential equations is the most important part of the theory of the nonlinear partial di?erential equations. In this article, we will discuss the blow-up properties of solutions to a nonlinear localized degenerate and singular parabolic equation and a nonlinear nonlocal degenerate and singular parabolic equation with weighted nonlocal boundary conditions.Firstly, discussing the blow-up properties of solution to a nonlinear localized degenerate and singular parabolic equation with weighted nonlocal boundary conditions, by established the comparison principle and constructed the supersolution and subsolution, we can obtain some appropriate conditions for the global existence, blow-up in ?nite time, global blow-up, and we also give out the blow-up set of the solution.Secondly, investigating the blow-up properties of solution to a nonlinear nonlocal degenerate and singular parabolic equation with weighted nonlocal boundary conditions. Under the appropriate hypothesis, by establishing the comparison principle and constructing the supersolution and subsolution, and by using the eigenfunctions method and Green function s properties, we also get the global existence, blow-up in ?nite time, global blow-up and result that the blow-up set is the whole domain.