The authors study homogenization of some nonlinear partial differential equations of the form -div (a (hx, h^2x, Duh))=f, where a is periodic in the first two arguments and monotone in the third. In particular the c...The authors study homogenization of some nonlinear partial differential equations of the form -div (a (hx, h^2x, Duh))=f, where a is periodic in the first two arguments and monotone in the third. In particular the case where a satisfies degenerated structure conditions is studied.It is proved that uh converges weakly in W0^1,1 (Ω) to the unique solution of a limit problem as h→＋∞. Moreover, explicit expressions for the limit problem are obtained.展开更多
This paper is a continuation of the authors' previous paper [1].In this paper the authors prove,assuming additional conditions on the initial data,some results about the existence and uniqueness of the entropy wea...This paper is a continuation of the authors' previous paper [1].In this paper the authors prove,assuming additional conditions on the initial data,some results about the existence and uniqueness of the entropy weak solutions of the Cauchy problem for the singular hyperbolic system at + (au)x + 2aux = 0, x＞0,t≥0. ut + 1/2 (a2 + u2)x = o,展开更多
文摘The authors study homogenization of some nonlinear partial differential equations of the form -div (a (hx, h^2x, Duh))=f, where a is periodic in the first two arguments and monotone in the third. In particular the case where a satisfies degenerated structure conditions is studied.It is proved that uh converges weakly in W0^1,1 (Ω) to the unique solution of a limit problem as h→＋∞. Moreover, explicit expressions for the limit problem are obtained.
文摘This paper is a continuation of the authors' previous paper [1].In this paper the authors prove,assuming additional conditions on the initial data,some results about the existence and uniqueness of the entropy weak solutions of the Cauchy problem for the singular hyperbolic system at + (au)x + 2aux = 0, x＞0,t≥0. ut + 1/2 (a2 + u2)x = o,
