Blow-up And Global Existence For Two Classes Of Nonlinear Parabolic Equations With Nonlocal Terms

The study of nonlinear parabolic equations play an important role in the research of partial differential equations,and the global existence and blow-up of its solutions are of great significance.Two classes of the properties of the nonlinear parabolic equation solutions are studied.One class is the global existence and the blow up of the definite solutions of the p-laplacian equation with a nonlocal weighted term,and the other class is the blow up of the definite solutions of the p-laplacian equation with time-dependent coefficient terms.For the first class of the p-laplacian equations with nonlocal weighted term,appropriate assumptions are made about the functions,suitable auxiliary functions are constructed,and Sobolev inequality and differential inequality techniques are used to study and draw conclusions about the global existence and the blow up of the definite solutions of the equations.Under the nonlinear boundary conditions,the sufficient conditions are obtained for the global existence of the solutions of the equations in the sense of auxiliary functions,the upper bound of the blow up time of the solutions is obtained,and the lower bound of the blow up time of the solutions is obtained when N(29)2 and N(28)2.For the second class of the p-laplacian equations with time-dependent coefficient terms,appropriate auxiliary functions are constructed,the functions are assumed,and Sobolev inequality and differential inequality techniques are used to study the blow up of the definite solutions of the equations and draw relevant conclusions.Under nonlocal value conditions,the definite solutions of the equation blow up in finite time in the sense of an auxiliary function,and the upper bound of the blow up time is obtained,and the lower bound of the blow up time of the solutions is obtained when the blow-up occurs at N(29)2 and N(28)2.Finally,the two classes of the equations are summarized.A further research outlook for nonlinear parabolic equations is proposed based on the research conclusions,and a research direction of nonlinear parabolic equations is put forward.