The existence and uniqueness of the state for 2 × 2 Dirichlet cooperative elliptic systems under conjugation conditions are proved using Lax-Milgram lemma, then the boundary control for these systems is discussed...The existence and uniqueness of the state for 2 × 2 Dirichlet cooperative elliptic systems under conjugation conditions are proved using Lax-Milgram lemma, then the boundary control for these systems is discussed. The set of equations and inequalities that characterizes this boundary control is found by theory of Lions, Sergienko and Deineka. The problem for cooperative Neumann elliptic systems under conjugation conditions is also considered. Finally, the problem for <em>n</em> × <em>n</em> cooperative elliptic systems under conjugation conditions is established.展开更多
In this paper,we establish the lower bounds estimate of the blow up time for solutions to the nonlocal cross-coupled porous medium equations with nonlocal source terms under Dirichlet and Neumann boundary conditions.T...In this paper,we establish the lower bounds estimate of the blow up time for solutions to the nonlocal cross-coupled porous medium equations with nonlocal source terms under Dirichlet and Neumann boundary conditions.The results are obtained by using some differential inequality technique.展开更多
New direct spectral solvers for the 3D Helmholtz equation in a finite cylindrical region are presented.A purely variational(no collocation)formulation of the problem is adopted,based on Fourier series expansion of the...New direct spectral solvers for the 3D Helmholtz equation in a finite cylindrical region are presented.A purely variational(no collocation)formulation of the problem is adopted,based on Fourier series expansion of the angular dependence and Legendre polynomials for the axial dependence.A new Jacobi basis is proposed for the radial direction overcoming the main disadvantages of previously developed bases for the Dirichlet problem.Nonhomogeneous Dirichlet boundary conditions are enforced by a discrete lifting and the vector problem is solved by means of a classical uncoupling technique.In the considered formulation,boundary conditions on the axis of the cylindrical domain are never mentioned,by construction.The solution algorithms for the scalar equations are based on double diagonalization along the radial and axial directions.The spectral accuracy of the proposed algorithms is verified by numerical tests.展开更多
文摘The existence and uniqueness of the state for 2 × 2 Dirichlet cooperative elliptic systems under conjugation conditions are proved using Lax-Milgram lemma, then the boundary control for these systems is discussed. The set of equations and inequalities that characterizes this boundary control is found by theory of Lions, Sergienko and Deineka. The problem for cooperative Neumann elliptic systems under conjugation conditions is also considered. Finally, the problem for <em>n</em> × <em>n</em> cooperative elliptic systems under conjugation conditions is established.
基金supported by Natural Science Basic Research Project of Shaanxi Province(2019JM-534)Soft Science Project of Shaanxi Province(2019KRM169)+2 种基金Planned Projects of the 13th Five-year Plan for Education Science of Shaanxi Province(SGH18H544)Project on Higher Education Teaching Reform of Xi'an International University(2019B36)the Youth Innovation Team of Shaanxi Universities.
文摘In this paper,we establish the lower bounds estimate of the blow up time for solutions to the nonlocal cross-coupled porous medium equations with nonlocal source terms under Dirichlet and Neumann boundary conditions.The results are obtained by using some differential inequality technique.
文摘New direct spectral solvers for the 3D Helmholtz equation in a finite cylindrical region are presented.A purely variational(no collocation)formulation of the problem is adopted,based on Fourier series expansion of the angular dependence and Legendre polynomials for the axial dependence.A new Jacobi basis is proposed for the radial direction overcoming the main disadvantages of previously developed bases for the Dirichlet problem.Nonhomogeneous Dirichlet boundary conditions are enforced by a discrete lifting and the vector problem is solved by means of a classical uncoupling technique.In the considered formulation,boundary conditions on the axis of the cylindrical domain are never mentioned,by construction.The solution algorithms for the scalar equations are based on double diagonalization along the radial and axial directions.The spectral accuracy of the proposed algorithms is verified by numerical tests.
