Existence Of Solutions To A Class Of Thin-film Equations With Logarithmic Nonlinear Term

In this thesis,we consider a class of thin-film equations with logarithmic nonlinear term,namely the following initial boundary problem for fourth-order parabolic(?) where ?=(-a,a),a ? R+.{u>0}={(t,x)? R+×?:u(t,x)>0},p>2,n?(p-1/2,2p-1).Based on the methods of Ansini and Giacomelli,firstly,we replace un by non-linearities which are bounded and strongly degenerate at u=0,and add artificial regularizing terms in the equation to change the original equation into the following Neumann boundary value problem(?).Then the Galerkin method is used to construct the approximating solutions,and a series of uniform estimates of the approximating solutions are made by means of energy estimates and Bernis' inequalities.Finally,we obtain a solution to the problem on bounded regions after the multi-step approximating procedure.