A one-phase Stefan problem for the nonhomogeneous heat equation with the source term depending on an unknown parameter p(t) is considered. The existence and uniqueness of the solution (p, s, u) are also demonstrated.
In this paper we consider an evolutionary continuous casting problem with convection partial derivative + b(y) chi - Delta kappa(u) + (v) over right arrow .del u = 0 coupled with Stokes equation in the liquid phase pa...In this paper we consider an evolutionary continuous casting problem with convection partial derivative + b(y) chi - Delta kappa(u) + (v) over right arrow .del u = 0 coupled with Stokes equation in the liquid phase partial derivative(t) (v) over right arrow - v Delta (v) over right arrow + del p = (f) over right arrow(u) The mixed boundary condition is put on temprature. The existence of a weak solution is obtained by using methods of regularization, temperature dependent penalty form in the Stokes equation and compact arguments.展开更多
文摘A one-phase Stefan problem for the nonhomogeneous heat equation with the source term depending on an unknown parameter p(t) is considered. The existence and uniqueness of the solution (p, s, u) are also demonstrated.
文摘In this paper we consider an evolutionary continuous casting problem with convection partial derivative + b(y) chi - Delta kappa(u) + (v) over right arrow .del u = 0 coupled with Stokes equation in the liquid phase partial derivative(t) (v) over right arrow - v Delta (v) over right arrow + del p = (f) over right arrow(u) The mixed boundary condition is put on temprature. The existence of a weak solution is obtained by using methods of regularization, temperature dependent penalty form in the Stokes equation and compact arguments.
