共查询到20条相似文献,搜索用时 93 毫秒
1.
Mahesh Nerurkar 《Journal of Dynamics and Differential Equations》2011,23(3):451-473
Consider the class of C
r
-smooth
SL(2, \mathbb R){SL(2, \mathbb R)} valued cocycles, based on the rotation flow on the two torus with irrational rotation number α. We show that in this class,
(i) cocycles with positive Lyapunov exponents are dense and (ii) cocycles that are either uniformly hyperbolic or proximal
are generic, if α satisfies the following Liouville type condition:
|a-\fracpnqn| £ C exp (-qr+1+kn)\left|\alpha-\frac{p_n}{q_n}\right| \leq C {\rm exp} (-q^{r+1+\kappa}_{n}), where C > 0 and 0 < k < 1{0 < \kappa <1 } are some constants and
\fracPnqn{\frac{P_n}{q_n}} is some sequence of irreducible fractions. 相似文献
2.
In this study, fully developed heat and fluid flow in a parallel plate channel partially filled with porous layer is analyzed
both analytically and numerically. The porous layer is located at the center of the channel and uniform heat flux is applied
at the walls. The heat and fluid flow equations for clear fluid and porous regions are separately solved. Continues shear
stress and heat flux conditions at the interface are used to determine the interface velocity and temperature. The velocity
and temperature profiles in the channel for different values of Darcy number, thermal conductivity ratio, and porous layer
thickness are plotted and discussed. The values of Nusselt number and friction factor of a fully clear fluid channel (Nu
cl = 4.12 and fRe
cl = 24) are used to define heat transfer increment ratio (eth = Nup/Nucl)({\varepsilon _{\rm th} =Nu_{\rm p}/Nu_{\rm cl})} and pressure drop increment ratio (ep = fRep/fRecl )({\varepsilon_{\rm p} =fRe_{\rm p}/fRe_{\rm cl} )} and observe the effects of an inserted porous layer on the increase of heat transfer and pressure drop. The heat transfer
and pressure drop increment ratios are used to define an overall performance (e = eth/ep)({\varepsilon = \varepsilon_{\rm th}/\varepsilon_{\rm p})} to evaluate overall benefits of an inserted porous layer in a parallel plate channel. The obtained results showed that for
a partially porous filled channel, the value of e{\varepsilon} is highly influenced from Darcy number, but it is not affected from thermal conductivity ratio (k
r) when k
r > 2. For a fully porous material filled channel, the value of e{\varepsilon} is considerably affected from thermal conductivity ratio as the porous medium is in contact with the channel walls. 相似文献
3.
This paper deals with the rational function approximation of the irrational transfer function
G(s) = \fracX(s)E(s) = \frac1[(t0s)2m + 2z(t0s)m + 1]G(s) = \frac{X(s)}{E(s)} = \frac{1}{[(\tau _{0}s)^{2m} + 2\zeta (\tau _{0}s)^{m} + 1]} of the fundamental linear fractional order differential equation
(t0)2m\fracd2mx(t)dt2m + 2z(t0)m\fracdmx(t)dtm + x(t) = e(t)(\tau_{0})^{2m}\frac{d^{2m}x(t)}{dt^{2m}} + 2\zeta(\tau_{0})^{m}\frac{d^{m}x(t)}{dt^{m}} + x(t) = e(t), for 0<m<1 and 0<ζ<1. An approximation method by a rational function, in a given frequency band, is presented and the impulse and
the step responses of this fractional order system are derived. Illustrative examples are also presented to show the exactitude
and the usefulness of the approximation method. 相似文献
4.
Craig Cowan Pierpaolo Esposito Nassif Ghoussoub Amir Moradifam 《Archive for Rational Mechanics and Analysis》2010,198(3):763-787
We study the regularity of the extremal solution of the semilinear biharmonic equation ${{\Delta^2} u=\frac{\lambda}{(1-u)^2}}We study the regularity of the extremal solution of the semilinear biharmonic equation
D2 u=\fracl(1-u)2{{\Delta^2} u=\frac{\lambda}{(1-u)^2}}, which models a simple micro-electromechanical system (MEMS) device on a ball
B ì \mathbbRN{B\subset{\mathbb{R}}^N}, under Dirichlet boundary conditions u=?n u=0{u=\partial_\nu u=0} on ?B{\partial B}. We complete here the results of Lin and Yang [14] regarding the identification of a “pull-in voltage” λ* > 0 such that a stable classical solution u
λ with 0 < u
λ < 1 exists for l ? (0,l*){\lambda\in (0,\lambda^*)}, while there is none of any kind when λ > λ*. Our main result asserts that the extremal solution ul*{u_{\lambda^*}} is regular (supB ul* < 1 ){({\rm sup}_B u_{\lambda^*} <1 )} provided
N \leqq 8{N \leqq 8} while ul*{u_{\lambda^*}} is singular (supB ul* = 1){({\rm sup}_B u_{\lambda^*} =1)} for
N \geqq 9{N \geqq 9}, in which case
1-C0|x|4/3 \leqq ul* (x) \leqq 1-|x|4/3{1-C_0|x|^{4/3} \leqq u_{\lambda^*} (x) \leqq 1-|x|^{4/3}} on the unit ball, where
C0:=(\fracl*[`(l)])\frac13{C_0:=\left(\frac{\lambda^*}{\overline{\lambda}}\right)^\frac{1}{3}} and
[`(l)]: = \frac89(N-\frac23)(N- \frac83){\bar{\lambda}:= \frac{8}{9}\left(N-\frac{2}{3}\right)\left(N- \frac{8}{3}\right)}. 相似文献
5.
C. Grotta-Ragazzo Coraci Pereira Malta K. Pakdaman 《Journal of Dynamics and Differential Equations》2010,22(2):203-252
We consider the scalar delayed differential equation e[(x)\dot](t)=-x(t) +f(x(t-1)){\epsilon\dot x(t)=-x(t)\,+f(x(t-1))}, where ${\epsilon\,{>}\,0}${\epsilon\,{>}\,0} and f verifies either df/dx > 0 or df/dx < 0 and some other conditions. We present theorems indicating that a generic initial condition with sign changes generates
a solution with a transient time of order exp(c/e){{\rm exp}(c{/}\epsilon)}, for some c > 0. We call it a metastable solution. During this transient a finite time span of the solution looks like that of a periodic
function. It is remarkable that if df/dx > 0 then f must be odd or present some other very special symmetry in order to support metastable solutions, while this condition is
absent in the case df/dx < 0. Explicit e{\epsilon}-asymptotics for the motion of zeroes of a solution and for the transient time regime are presented. 相似文献
6.
The effects of radiative losses on the thermal behavior of thin metal films, as described by the microscopic two-step hyperbolic heat conduction model, are investigated. Different criteria, which determine the ranges within which thermal radiative losses are significant, are derived. It is found that radiative losses from the electron gas are significant in thin films having [(CR ee4/3 T¥ 4 )/(ke1/3 L2/3 G)] 3 4.6 ×107{{C_R \epsilon _e^{{4 \over 3}} T_\infty ^4 } \over {k_e^{{1 \over 3}} L^{{2 \over 3}} G}}\geq 4.6 \times 10^7 for /o > 4 and FF < 1 and [(CR ee3/2 T¥ 9/2)/(ke1/2 L1/2 G)] 3 7.4 ×1010{{C_R \epsilon _e^{{3 \over 2}} T_\infty ^{{9 \over 2}}} \over {k_e^{{1 \over 2}} L^{{1 \over 2}} G}}\geq 7.4 \times 10^{10} for /o < 4 and FF > 1. 相似文献
7.
Vieri Benci Marco Ghimenti Anna Maria Micheletti 《Archive for Rational Mechanics and Analysis》2012,205(2):467-492
We study the behavior of the soliton solutions of the equation i\frac?y?t = - \frac12m Dy+ \frac12We¢(y) + V(x)y,i\frac{\partial\psi}{{\partial}t} = - \frac{1}{2m} \Delta\psi + \frac{1}{2}W_{\varepsilon}^{\prime}(\psi) + V(x){\psi}, 相似文献
8.
Fix a strictly increasing right continuous with left limits function ${W: \mathbb{R} \to \mathbb{R}}Fix a strictly increasing right continuous with left limits function
W: \mathbbR ? \mathbbR{W: \mathbb{R} \to \mathbb{R}} and a smooth function
F: [l,r] ? \mathbb R{\Phi : [l,r] \to \mathbb R}, defined on some interval [l, r] of
\mathbb R{\mathbb R}, such that
0 < b\leqq F¢\leqq b-1{0 < b\leqq \Phi'\leqq b^{-1}}. On the diffusive time scale, the evolution of the empirical density of exclusion processes with conductances given by W is described by the unique weak solution of the non-linear differential equation ?t r = (d/dx)(d/dW) F(r){\partial_t \rho = ({\rm d}/{\rm d}x)({\rm d}/{\rm d}W) \Phi(\rho)}. We also present some properties of the operator (d/dx)(d/dW). 相似文献
9.
This paper presents an existence and stability theory for gravity-capillary solitary waves on the surface of a body of water
of infinite depth. Exploiting a classical variational principle, we prove the existence of a minimiser of the wave energy
E{{\mathcal E}} subject to the constraint I=?2m{{\mathcal I}=\sqrt{2}\mu}, where I{{\mathcal I}} is the wave momentum and 0 < m << 1{0 < \mu \ll 1} . Since E{{\mathcal E}} and I{{\mathcal I}} are both conserved quantities a standard argument asserts the stability of the set D
μ
of minimisers: solutions starting near D
μ
remain close to D
μ
in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water
waves of the present kind are modelled as solutions of the nonlinear Schr?dinger equation with cubic focussing nonlinearity.
We show that the waves detected by our variational method converge (after an appropriate rescaling) to solutions of this model
equation as mˉ 0{\mu \downarrow 0} . 相似文献
10.
In this work, positive solutions to a doubly nonlinear parabolic equation with a nonlinear boundary condition are considered.
We study the problem where 0 < m, r, α < ∞ are parameters. It is known that for some values of the parameters there are solutions that blow up in finite time.
We determine in terms of α ,m, r the blow-up sets for these solutions. We prove that single point blow-up occurs if
max{m, r} < α,
global blow-up appears for the range of parameters
0 < m < α < r
and regional blow-up takes place if
0 < m < α = r and .
In this case the blow-up set consists of the interval . 相似文献
11.
We analyze the quasiperiodic damped Mathieu equation
[(x)\ddot]+ g[(x)\dot]+ x ( 1 + d+ eq(t) )=0 ,\ddot{x}+ \gamma\dot{x}+ x \bigl( 1 + \delta+ \epsilon q(t) \bigr )=0 , 相似文献
12.
In this paper we study the following coupled Schr?dinger system, which can be seen as a critically coupled perturbed Brezis–Nirenberg problem: {ll-Du +l1 u = m1 u3+buv2, x ? W,-Dv +l2 v = m2 v3+bvu2, x ? W,u\geqq 0, v\geqq 0 in W, u=v=0 on ?W.\left\{\begin{array}{ll}-\Delta u +\lambda_1 u = \mu_1 u^3+\beta uv^2, \quad x\in \Omega,\\-\Delta v +\lambda_2 v =\mu_2 v^3+\beta vu^2, \quad x\in \Omega,\\u\geqq 0, v\geqq 0\, {\rm in}\, \Omega,\quad u=v=0 \quad {\rm on}\, \partial\Omega.\end{array}\right. 相似文献
13.
We prove a regularity result for the anisotropic linear elasticity equation ${P u := {\rm div} \left( \boldmath\mathsf{C} \cdot \nabla u\right) = f}
14.
Enzo Vitillaro 《Archive for Rational Mechanics and Analysis》1999,149(2):155-182
We study abstract evolution equations with nonlinear damping terms and source terms, including as a particular case a nonlinear wave equation of the type $ \ba{cl} u_{tt}-\Delta u+ b|u_t|^{m-2}u_t=c|u|^{p-2}u, &;(t,x)\in [0,T)\times\Omega,\\[6pt] u(t,x)=0, &;(t,x)\in [0,T)\times\partial \Omega,\\[6pt] u(0,\cdot)=u_0\in H_0^1(\Omega), \quad u_t(0,\cdot)=v_0\in L^2(\Omega),\es&; \ea $ \ba{cl} u_{tt}-\Delta u+ b|u_t|^{m-2}u_t=c|u|^{p-2}u, &;(t,x)\in [0,T)\times\Omega,\\[6pt] u(t,x)=0, &;(t,x)\in [0,T)\times\partial \Omega,\\[6pt] u(0,\cdot)=u_0\in H_0^1(\Omega), \quad u_t(0,\cdot)=v_0\in L^2(\Omega),\es&; \ea where 0 < T £ ¥0
15.
H. J. Choe 《Journal of Mathematical Fluid Mechanics》2000,2(2):151-184
16.
Let Ω be a bounded smooth domain in ${{\bf R}^N, N\geqq 3}
|