一个对流扩散系统的解的衰减性

本文先构造出线性系统的近似解序列,并利用近似解的率减性结果给出了向量对流扩散方程ut-γΔu=-(｜u｜p-2u·)u在RN中的柯西问题的解的衰减性以及存在性.     

Decay estimates for a class of wave equations

In this paper we use a unified way studying the decay estimate for a class of dispersive semigroup given by , where is smooth away from the origin. Especially, the decay estimates for the solutions of the Klein-Gordon equation and the beam equation are simplified and slightly improved.     

Decay of global solutions of two nonlinear evolution equations

1.IntroductionTherehavebeenconsiderableliteratuxeonthedecayofsolutionstothebestialvalueproblemsforsomenonlinearevolutionequations[3,4,6,7,161.Undercertainassumptions,LZdecayandLoodecayofsolutionstotheseproblemswereestablished.Thereadersinterestedcanfindsuchworksinourreferences.OurillterestisfocusedonthedecayofsolutionsoftheinitialvalueproblemsfornonlinearBenjamin--OnthBurgers(BOB)l"'19--21]andSchlodinger-Burgers(SB)equationwhereHisHilberttransform,definedbyWewallttoshowthattheLZandLoon…     

Strong uniqueness for the plate equations

In this paper we show the strong uniqueness for the plate equations. By using the idea due to Lebeau we transform the given operator to the elliptic operators to which we apply the Carleman estimates given by Alinhac and Lerner.

     

Decay and growth estimates for solutions of second-order and third-order differential-operator equations

We obtained decay and growth estimates for solutions of second-order and third-order differential-operator equations in a Hilbert space. Applications to initial–boundary value problems for linear and nonlinear non-stationary partial differential equations modeling the strongly damped nonlinear improved Boussinesq equation, the dual-phase-lag heat conduction equations, the equation describing wave propagation in relaxing media, and the Moore–Gibson–Thompson equation are given.     

Non-Uniform Decay of MHD Equations With and Without Magnetic Diffusion

We consider the long time behavior of solutions to the magnetohydrodynamics equations in two and three spatial dimensions. It is shown that in the absence of magnetic diffusion, if strong bounded solutions were to exist their energy cannot present any asymptotic oscillatory behavior, the diffusivity of the velocity is enough to prevent such oscillations. When magnetic diffusion is present and the data is only in L ², it is shown that the solutions decay to zero without a rate, and this nonuniform decay is optimal.     

Boundary integral equations for bending of thermoelastic plates with transmission boundary conditions

The solution of an initial‐boundary value problem for bending of a piecewise‐homogeneous thermoelastic plate with transverse shear deformation is represented as various combinations of single‐layer and double‐layer time‐dependent potentials. The unique solvability of the boundary integral equations generated by these representations is proved in spaces of distributions. Copyright © 2009 John Wiley & Sons, Ltd.     

Decay and scattering of small solutions for Rosenau equations

We study the long-time behavior of small solutions of the Cauchy problem for a Rosenau equation. For a class of nonlinearity of the perturbation, the global small solution was obtained, and the decay and scattering for small amplitude solution are established.     

Decay estimates for dissipative wave equations in exterior domains

Consider the initial boundary value problem for the linear dissipative wave equation (□+∂_t)u=0 in an exterior domain . Using the so-called cut-off method together with local energy decay and L² decays in the whole space, we study decay estimates of the solutions. In particular, when N?3, we derive L^p decays with p?1 of the solutions. Next, as an application of the decay estimates for the linear equation, we consider the global solvability problem for the semilinear dissipative wave equations (□+∂_t)u=f(u) with f(u)=|u|^α+1,|u|^αu in an exterior domain.     

The Decay Rates of Strong Solutions for Navier-Stokes Equations

In this paper, we deduce the estimates on decay rates of higher order derivatives about time variable and space variables for the strong solution to the Cauchy problem of the Navier-Stokes equations. The rate obtained is optimal in the sense that it coincides with that of solution to the heat equation.     

Decay rates of solutions to a P1-approximation model arising from radiation hydrodynamics

This paper is concerned with the global existence and large time behavior of solutions to Cauchy problem for a P1-approximation radiation hydrodynamics model. The global-in-time existence result is established in the small perturbation framework around a stable radiative equilibrium states in Sobolev space $H^4({\mathbb{R}}^3)$. Moreover, when the initial perturbation is also bounded in $L^1({\mathbb{R}}^3)$, the $L^2$-decay rates of the solution and its derivatives are achieved accordingly. The proofs are based on the Littlewood–Paley decomposition techniques and elaborate energy estimates in different frequency regimes.     

Input dynamics and nonstandard riccati equations with applications to boundary control of damped wave and plate equations

An optimization problem for a control system governed by an analytic generator with unbounded control actions is considered. The solution to this problem is synthesized in terms of the Riccati operator, arising from a nonstandard Riccati equation. Solvability and uniqueness of the solutions to this Riccati equation are established. This theory is applied to a boundary control problem governed by damped wave and plate equations.Research of this author partially supported by NSF Grant DMS 9204338.     

Computational analysis of rates of energy decay in elastic beams

This paper is concerned with the damping of elastic beams of two different kinds. The first model involves the application of viscous damping at a single point either in the interior or at the boundary. The second involves a thermoelastic beam model in which mechanical damping is applied at a boundary. Since the second model is known to be uniformly stabilized via thermal effects alone, an analysis of the relative importance of the thermal and applied mechanical damping is presented. A careful analysis of the effects of rotational forces is also included using realistic model parameters.     

Decay rates for memory‐type plate system with delay and source term

In this paper, we consider a plate equation with infinite memory in the presence of delay and source term. Under suitable conditions on the delay and source term, we establish an explicit and general decay rate result without imposing restrictive assumptions on the behavior of the relaxation function at infinity. Our result allows a wider class of relaxation functions and improves earlier results in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Boundary feedback stabilization of coupled sine-Gordon equations

^** Email: koba{at}cntl.kyutech.ac.jp^*** Email: sakamoto{at}cntl.kyutech.ac.jp This paper is concerned with global stabilization of the systemgoverned by coupled sine-Gordon equations without damping. Astabilizer is constructed by boundary velocity feedback. Theclosed-loop system is shown to be well posed by the non-linearsemigroup approach. Moreover, using a multiplier method, globalexponential stabilization of the closed-loop system is proved.