THE FIRST BOUNDARY VALUE PROBLEM FOR QUASILINEAR DEGENERATE PARABOLIC EQUATIONS OF SECOND ORDER IN SEVERAL SPACE VARIABLES

【摘要】 <正> In this paper,we study the first boundary value problem for quasilinear equations ofthe formUnder certain conditions,the existence of generalized solutions in BV is proved by meansof the method of parabolic regularization.To do this,we need some estimates on the family{u_ε}of solutions of regularized problems and the most difficult step is to estimate|grad u_ε|L¹⁺In addition,some results on the uniqueness and stability of generalized solutions areestablished.更多还原

【Abstract】 In this paper,we study the first boundary value problem for quasilinear equations of the form Under certain conditions,the existence of generalized solutions in BV is proved by means of the method of parabolic regularization.To do this,we need some estimates on the family {u_ε}of solutions of regularized problems and the most difficult step is to estimate|grad u_ε|L¹⁺ In addition,some results on the uniqueness and stability of generalized solutions are established.更多还原