544 research outputs found
Existence and Decay of Solutions of a Nonlinear Viscoelastic Problem with a Mixed Nonhomogeneous Condition
We study the initial-boundary value problem for a nonlinear wave equation
given by u_{tt}-u_{xx}+\int_{0}^{t}k(t-s)u_{xx}(s)ds+ u_{t}^{q-2}u_{t}=f(x,t,u)
, 0 < x < 1, 0 < t < T, u_{x}(0,t)=u(0,t), u_{x}(1,t)+\eta u(1,t)=g(t),
u(x,0)=\^u_{0}(x), u_{t}(x,0)={\^u}_{1}(x), where \eta \geq 0, q\geq 2 are
given constants {\^u}_{0}, {\^u}_{1}, g, k, f are given functions. In part I
under a certain local Lipschitzian condition on f, a global existence and
uniqueness theorem is proved. The proof is based on the paper [10] associated
to a contraction mapping theorem and standard arguments of density. In Part} 2,
under more restrictive conditions it is proved that the solution u(t) and its
derivative u_{x}(t) decay exponentially to 0 as t tends to infinity.Comment: 26 page
The regularity and exponential decay of solution for a linear wave equation associated with two-point boundary conditions
This paper is concerned with the existence and the regularity of global
solutions to the linear wave equation associated with two-point type boundary
conditions. We also investigate the decay properties of the global solutions to
this problem by the construction of a suitable Lyapunov functional.Comment: 18 page
Existence, blow-up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two-point type
This paper is devoted to study a nonlinear wave equation with boundary
conditions of two-point type. First, we state two local existence theorems and
under suitable conditions, we prove that any weak solutions with negative
initial energy will blow up in finite time. Next, we give a sufficient
condition to guarantee the global existence and exponential decay of weak
solutions. Finally, we present numerical resultsComment: 2
Large time behavior of differential equations with drifted periodic coefficients modeling Carbon storage in soil
This paper is concerned with the linear ODE in the form
, which represents a simplified
storage model of the carbon in the soil. In the first part, we show that, for a
periodic function , a linear drift in the coefficient involves
a linear drift for the solution of this ODE. In the second part, we extend the
previous results to a classical heat non-homogeneous equation. The connection
with an analytic semi-group associated to the ODE equation is considered in the
third part. Numerical examples are given.Comment: 18 page
CAMELLIA THUANANA (CAMELLIA SECT. CHRYSANTHA) – A NEW SPECIES FROM THE CENTRAL HIGHLANDS, VIETNAM
Camellia thuanana, a new species of the genus Camellia L. (Theaceae) is described and illustrated from the Central Highlands, Vietnam. Morphological features of this species are small flowers and pedicellate; leaves stalked, anastomosing venation, blades oblong-elliptic to elliptic, sparsely hirsute along the midrib below; pedicel very short; bracteoles 2–3, triangular; sepals 4–(5) in opposite pairs; corolla light greenish-yellow color; petals 7–8, glabrous; androecium 190–200 stamens, light yellow, in 3–4 circles; gynoecium 3, ovary ovoid and pubescent; styles 3, free to the base, and glabrous. C. thuanana resembles C. thuongiana in some morphological characteristics. C. thuanana is classified into sect. Chrysantha by styles completely free, flowers yellow, ovaries 3–5 locular, and partially connate. The IUCN Redlist Category of C. thuanana was assessed as Critically Endangered (CR)
Stabilization for equal-order polygonal finite element method for high fluid velocity and pressure gradient
This paper presents an adapted stabilisation method for the equal-order mixed scheme of finite elements on convex polygonal meshes to analyse the high velocity and pressure gradient of incompressible fluid flows that are governed by Stokes equations system. This technique is constructed by a local pressure projection which is extremely simple, yet effective, to eliminate the poor or even non-convergence as well as the instability of equal-order mixed polygonal technique. In this research, some numerical examples of incompressible Stokes fluid flow that is coded and programmed by MATLAB will be presented to examine the effectiveness of the proposed stabilised method
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