The 3D navier-stokes equations seen as a perturbation of the 2D navier-stokes equations
The a priori estimate of the maximum modulus to solutions of doubly nonlinear parabolic equations
The a priori estimate of the maximum modulus of the generalized solution is established for a doubly nonlinear parabolic equation with special structural conditions.
The Absolute Continuity of Elliptic Measure Revisited.
The accuracy of Dafermos' method for nonlinear hyperbolic equations
The accuracy of numerically computed orbits of dynamical systems
The algebraic Bethe Ansatz and vacuum vectors.
The Algebraic Multiplicity of Eigenvalues and the Evans Function Revisited
This paper is related to the spectral stability of traveling wave solutions of partial differential equations. In the first part of the paper we use the Gohberg-Rouche Theorem to prove equality of the algebraic multiplicity of an isolated eigenvalue of an abstract operator on a Hilbert space, and the algebraic multiplicity of the eigenvalue of the corresponding Birman-Schwinger type operator pencil. In the second part of the paper we apply this result...
The algebro-geometric Toda hierarchy initial value problem for complex-valued initial data.
The Allegretto-Piepenbrink theorem for strongly local Dirichlet forms.
The analysis of blow-up solutions to a semilinear parabolic system with weighted localized terms
This paper deals with blow-up properties of solutions to a semilinear parabolic system with weighted localized terms, subject to the homogeneous Dirichlet boundary conditions. We investigate the influence of the three factors: localized sources , vⁿ(x₀,t), local sources , , and weight functions a(x),b(x), on the asymptotic behavior of solutions. We obtain the uniform blow-up profiles not only for the cases m,q ≤ 1 or m,q > 1, but also for m > 1 q < 1 or m < 1 q > 1.
The analysis of intergrid transfer operators and multigrid methods for nonconforming finite elements.
The anti-disturbance property of a closed-loop system of 1-d wave equation with boundary control matched disturbance
We study the anti-disturbance problem of a 1-d wave equation with boundary control matched disturbance. In earlier literature, the authors always designed the controller such as the sliding mode control and the active disturbance rejection control to stabilize the system. However, most of the corresponding closed-loop systems are boundedly stable. In this paper we show that the linear feedback control also has a property of anti-disturbance, even if the disturbance includes some information of the...
The application of Picone-type identity for some nonlinear elliptic differential equations.
The approximate Riemann solver of Roe applied to a drift-flux two-phase flow model
We construct a Roe-type numerical scheme for approximating the solutions of a drift-flux two-phase flow model. The model incorporates a set of highly complex closure laws, and the fluxes are generally not algebraic functions of the conserved variables. Hence, the classical approach of constructing a Roe solver by means of parameter vectors is unfeasible. Alternative approaches for analytically constructing the Roe solver are discussed, and a formulation of the Roe solver valid for general closure...
The area preserving curve shortening flow with Neumann free boundary conditions
We study the area preserving curve shortening flow with Neumann free boundary conditions outside of a convex domain in the Euclidean plane. Under certain conditions on the initial curve the flow does not develop any singularity, and it subconverges smoothly to an arc of a circle sitting outside of the given fixed domain and enclosing the same area as the initial curve.
The asymptotic behavior at the large time of solutions of some mathematical physics problems
The asymptotic behaviour of surfaces with prescribed mean curvature near meeting points of fixed and free boundaries
We study the shape of stationary surfaces with prescribed mean curvature in the Euclidean 3-space near boundary points where Plateau boundaries meet free boundaries. In deriving asymptotic expansions at such points, we generalize known results about minimal surfaces due to G. Dziuk. The main difficulties arise from the fact that, contrary to minimal surfaces, surfaces with prescribed mean curvature do not meet the support manifold perpendicularly along their free boundary, in general.
The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form
2000 Mathematics Subject Classification: 35J70, 35P15.The asymptotic of the first eigenvalue for linear second order elliptic equations in divergence form with large drift is studied. A necessary and a sufficient condition for the maximum possible rate of the first eigenvalue is proved.
The asymptotic stability of steady solutions of reaction-convection-diffusion equations.
The asymptotics for the number of eigenvalue branches for the magnetic Schrödinger operator H - ? W in a gap of H.