This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protoc...This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protocell in multidimensional case. The local classical solution of the problem with free boundary (?) y = g(x,t) between two domains is being seeked. The local existence and uniqueness of the problem will be proved in multidimensional case.展开更多
This paper is concerned with the free boundary value problem for multidimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. Local ...This paper is concerned with the free boundary value problem for multidimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. Local （in time） existence of a weak solution is established; in particular, the density is positive and the solution is regular away from the free boundary.展开更多
A two phase free boundary problem for coupled system including three elliptic equations is considered.The problem comes from the discussion of a growth model of self maintaining protocell in multidimensional case.Th...A two phase free boundary problem for coupled system including three elliptic equations is considered.The problem comes from the discussion of a growth model of self maintaining protocell in multidimensional case.The global classical solution of the problem with free boundary Γ∶y=g(x,t) between two domains is under search.The global existence and uniqueness of a quasi-stationary problem are proved in multidimensional case.展开更多
In this paper, we use contraction mapping principle, operator-theoretic approach and some uniform estimates to establish local solvability of the parabolic-hyperbolic type chemotaxis system with fixed boundary in 1-di...In this paper, we use contraction mapping principle, operator-theoretic approach and some uniform estimates to establish local solvability of the parabolic-hyperbolic type chemotaxis system with fixed boundary in 1-dimensional domain. In addition, local solvability of the free boundary problem is considered by straightening the free boundary.展开更多
基金The project is supported by National Natural Science Foundation of China(10371045)Guangdong Provincial Natural Science Foundation of China(000671)National Natural Science Foundation of China(10426015).
文摘This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protocell in multidimensional case. The local classical solution of the problem with free boundary (?) y = g(x,t) between two domains is being seeked. The local existence and uniqueness of the problem will be proved in multidimensional case.
基金partially supported by the NSFC(10871134)the AHRDIHL Project of Beijing Municipality (PHR201006107)
文摘This paper is concerned with the free boundary value problem for multidimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. Local （in time） existence of a weak solution is established; in particular, the density is positive and the solution is regular away from the free boundary.
文摘A two phase free boundary problem for coupled system including three elliptic equations is considered.The problem comes from the discussion of a growth model of self maintaining protocell in multidimensional case.The global classical solution of the problem with free boundary Γ∶y=g(x,t) between two domains is under search.The global existence and uniqueness of a quasi-stationary problem are proved in multidimensional case.
基金Supported by the National Natural Science Foundation of China(11131005)the Fundamental Research Funds for the Central Universities(2014201020202)
文摘In this paper, we use contraction mapping principle, operator-theoretic approach and some uniform estimates to establish local solvability of the parabolic-hyperbolic type chemotaxis system with fixed boundary in 1-dimensional domain. In addition, local solvability of the free boundary problem is considered by straightening the free boundary.
