A Class Of P-laplacian Elliptic Parabolic Equations Of The Existence And Uniqueness,

At present, the practical problems in such disciplines as physics, biochemistry, medicine and cybernetics can be resolved through the theory of partial differential equation. People have paid much attention to their study and got plenty of important results, which has promoted the maturity of the theory of partial differential equation.Based on previous researches, in Chapter 3 we prove the existence of solution to a class of nonlinear elliptic-parabolic equation, which reads Under some suitable conditions, by using the nature of subdifferential, we replace the L2 space used in [21] with the Lp space, p≥2. The conditions are weakened, therefore this method can be more widely used. In Chapter 4 we emphatically prove the existence and uniqueness of the solution to a class of p- Laplacian elliptic- parabolic equation, namely, Ifρt(u)≡O, the above equation reduces to an elliptic equation, while in the case thatρt(u)≥O, it becomes a parabolic one. We first transform the above equation into a subdifferential form, i.e.ρt(u)(t)+(?)φt(u(t))(?)f(t). Next, we obtain the conditions required by the existence problem and prove the existence resultls to the class of p - Laplacian elliptic-parabolic equation. Finally, we show the uniqueness of the solution by using its orderliness.