In this paper, we study the existence and nonuniqueness of weak solutions of the initial and boundary value problem for ut= uσdiv(|△u|p-2△u) with σ≥1. Localization property of weak solutions is also discussed.
In this paper, we prove the existence and nonuniqueness of the weak solutions of the initial and boundary value problem for a nonlinear degenerate parabolic equation not in divergence form. Localization property of we...In this paper, we prove the existence and nonuniqueness of the weak solutions of the initial and boundary value problem for a nonlinear degenerate parabolic equation not in divergence form. Localization property of weak solutions will be also discussed.展开更多
Let A be a symmetric and positive definite(1,1)tensor on a bounded domain Ω in an ndimensional metric measure space(R^n,<,>,e^-φdv).In this paper,we investigate the Dirichlet eigenvalue problem of a system of ...Let A be a symmetric and positive definite(1,1)tensor on a bounded domain Ω in an ndimensional metric measure space(R^n,<,>,e^-φdv).In this paper,we investigate the Dirichlet eigenvalue problem of a system of equations of elliptic operators in weighted divergence form{LA,φu+α▽(divu)-▽φdivu]=-su,inΩ,u∣aΩ=0,where LA,φ=div(A▽(·))-(A▽φ,▽(·)),α is a nonnegative constant and u is a vector-valued function.Some universal inequalities for eigenvalues of this problem are established.Moreover,as applications of these results,we give some estimates for the upper bound of sk+1 and the gap of sk+1-sk in terms of the first k eigenvalues.Our results contain some results for the Lam′e system and a system of equations of the drifting Laplacian.展开更多
We establish conditions of the nonexistence of weak solutions of the Dirich- let problem for nonlinear elliptic equations of arbitrary even order with some right- hand sides from Lm where m ~ 1. The conditions include...We establish conditions of the nonexistence of weak solutions of the Dirich- let problem for nonlinear elliptic equations of arbitrary even order with some right- hand sides from Lm where m ~ 1. The conditions include the requirement of a certain closeness of the parameter m to 1.展开更多
This article is devoted to establishing a least square based weak Galerkin method for second order elliptic equations in non-divergence form using a discrete weak Hessian operator.Naturally,the resulting linear system...This article is devoted to establishing a least square based weak Galerkin method for second order elliptic equations in non-divergence form using a discrete weak Hessian operator.Naturally,the resulting linear system is symmetric and positive definite,and thus the algorithm is easy to implement and analyze.Convergence analysis in the H2 equivalent norm is established on an arbitrary shape regular polygonal mesh.A superconvergence result is proved when the coefficient matrix is constant or piecewise constant.Numerical examples are performed which not only verify the theoretical results but also reveal some unexpected superconvergence phenomena.展开更多
This paper concerns with properties of solutions of a nonlinear diffusion problem in non-divergence form. By constructing proper test functions, it is proved that solutions of the problem possess the property of local...This paper concerns with properties of solutions of a nonlinear diffusion problem in non-divergence form. By constructing proper test functions, it is proved that solutions of the problem possess the property of localization.展开更多
基金The Young Teachers Foundation (420010302318) of Jilin University.
文摘In this paper, we study the existence and nonuniqueness of weak solutions of the initial and boundary value problem for ut= uσdiv(|△u|p-2△u) with σ≥1. Localization property of weak solutions is also discussed.
文摘In this paper, we prove the existence and nonuniqueness of the weak solutions of the initial and boundary value problem for a nonlinear degenerate parabolic equation not in divergence form. Localization property of weak solutions will be also discussed.
基金supported by the National Natural Science Foundation of China(Grant Nos.1100113011571361 and 11831005)the Fundamental Research Funds for the Central Universities(Grant No.30917011335)。
文摘Let A be a symmetric and positive definite(1,1)tensor on a bounded domain Ω in an ndimensional metric measure space(R^n,<,>,e^-φdv).In this paper,we investigate the Dirichlet eigenvalue problem of a system of equations of elliptic operators in weighted divergence form{LA,φu+α▽(divu)-▽φdivu]=-su,inΩ,u∣aΩ=0,where LA,φ=div(A▽(·))-(A▽φ,▽(·)),α is a nonnegative constant and u is a vector-valued function.Some universal inequalities for eigenvalues of this problem are established.Moreover,as applications of these results,we give some estimates for the upper bound of sk+1 and the gap of sk+1-sk in terms of the first k eigenvalues.Our results contain some results for the Lam′e system and a system of equations of the drifting Laplacian.
文摘We establish conditions of the nonexistence of weak solutions of the Dirich- let problem for nonlinear elliptic equations of arbitrary even order with some right- hand sides from Lm where m ~ 1. The conditions include the requirement of a certain closeness of the parameter m to 1.
基金supported by Zhejiang Provincial Natural Science Foundation of China(LY19A010008).
文摘This article is devoted to establishing a least square based weak Galerkin method for second order elliptic equations in non-divergence form using a discrete weak Hessian operator.Naturally,the resulting linear system is symmetric and positive definite,and thus the algorithm is easy to implement and analyze.Convergence analysis in the H2 equivalent norm is established on an arbitrary shape regular polygonal mesh.A superconvergence result is proved when the coefficient matrix is constant or piecewise constant.Numerical examples are performed which not only verify the theoretical results but also reveal some unexpected superconvergence phenomena.
文摘This paper concerns with properties of solutions of a nonlinear diffusion problem in non-divergence form. By constructing proper test functions, it is proved that solutions of the problem possess the property of localization.
