Quenching Phenomena Of Two Classes Of Nonlinear Parabolic Equations With Singular Boundary Conditions

This paper mainly studies the nonlinear parabolic equation and the two types of p-laplacian equation solution of equation with singular boundary conditions of quenching phenomenon,according to the two problems,we mainly use maximum principle,the theory of differential equation and complicated calculus to complete,in this article,we pass a certain assumptions to determine whether the two types of equations with quenching phenomenon,through the theory of differential equation we proved that the two types of equations can occur under the condition of a given beforehand quenching,finally we can estimate the equation of the two lower rate of quenching,quenching time.In chapter 1,we first briefly stated the background needed for this paper,and then briefly describe the research trends of some scholars on partial differential equations and quenching phenomenon in recent years.In addition,this chapter also explains the significance and purpose of studying quenching phenomenon in this paper.Finally,we make a simple summary of the main work and conclusions of this paper.In chapter 2,we mainly study the quenching phenomenon of solutions of semilinear parabolic equations with singular boundary fluxes.In this chapter,we use when time tends to be a fixed maximum value of the solution of the finite time when the equation 1this way to define the quenching,the initial of the given condition,we can judge the solution of this equation to quenching in limited time,when quenching phenomenon occurs when we know and estimate quenching rate lower,and the lower bound of quenching time we also can easy to push it.In chapter 3,we mainly study the quenching phenomenon of the solution of a class of p-laplacian equations.In this chapter we mainly according to two kinds of definition of quenching methods respectively to study the solution of the quenching phenomenon,including when in the first way to define quenching,we obtained under certain assumptions quenching phenomenon can occur in a limited time,and in this case,we get the quenching occurs when the solution quenching rate lower,at the same time,the lower bound of quenching time can be calculated.When quenching is defined in the second way,we obtain that the quenching phenomenon can also occur in finite time under certain hypothetical conditions,and in this case,we obtain the upper and lower bounds of the rate when quenching occurs.In chapter 4,we briefly summarize the quenching phenomenon of the solutions of two kinds of nonlinear parabolic equations with singular boundary conditions,and guide the following research directions of this paper..