共查询到20条相似文献,搜索用时 15 毫秒
1.
Olivier Lafitte Mark Williams Kevin Zumbrun 《Archive for Rational Mechanics and Analysis》2012,204(1):141-187
The rigorous study of spectral stability for strong detonations was begun by Erpenbeck (Phys. Fluids 5:604–614 1962). Working with the Zeldovitch–von Neumann–D?ring (ZND) model (more precisely, Erpenbeck worked with an extension of ZND to
general chemistry and thermodynamics), which assumes a finite reaction rate but ignores effects such as viscosity corresponding
to second order derivatives, he used a normal mode analysis to define a stability function V(t,e){V(\tau,\epsilon)} whose zeros in ${\mathfrak{R}\tau > 0}${\mathfrak{R}\tau > 0} correspond to multidimensional perturbations of a steady detonation profile that grow exponentially in time. Later in a remarkable
paper (Erpenbeck in Phys. Fluids 9:1293–1306, 1966; Stability of detonations for disturbances of small transverse wavelength, 1965) he provided strong evidence, by a combination of formal and rigorous arguments, that for certain classes of steady ZND profiles,
unstable zeros of V exist for perturbations of sufficiently large transverse wavenumber e{\epsilon} , even when the von Neumann shock, regarded as a gas dynamical shock, is uniformly stable in the sense defined (nearly 20 years
later) by Majda. In spite of a great deal of later numerical work devoted to computing the zeros of V(t,e){V(\tau,\epsilon)} , the paper (Erpenbeck in Phys. Fluids 9:1293–1306, 1966) remains one of the few works we know of [another is Erpenbeck (Phys. Fluids 7:684–696, 1964), which considers perturbations for which the ratio of longitudinal over transverse components approaches ∞] that presents
a detailed and convincing theoretical argument for detecting them. The analysis in Erpenbeck (Phys. Fluids 9:1293–1306, 1966) points the way toward, but does not constitute, a mathematical proof that such unstable zeros exist. In this paper we identify
the mathematical issues left unresolved in Erpenbeck (Phys. Fluids 9:1293–1306, 1966) and provide proofs, together with certain simplifications and extensions, of the main conclusions about stability and instability
of detonations contained in that paper. The main mathematical problem, and our principal focus here, is to determine the precise
asymptotic behavior as e?¥{\epsilon\to\infty} of solutions to a linear system of ODEs in x, depending on e{\epsilon} and a complex frequency τ as parameters, with turning points x
* on the half-line [0,∞). 相似文献
2.
Fractional calculus has gained a lot of importance during the last decades, mainly because it has become a powerful tool in
modeling several complex phenomena from various areas of science and engineering. This paper gives a new kind of perturbation
of the order of the fractional derivative with a study of the existence and uniqueness of the perturbed fractional-order evolution
equation for CDa-e0+u(t)=A CDd0+u(t)+f(t),^{C}D^{\alpha-\epsilon}_{0+}u(t)=A~^{C}D^{\delta}_{0+}u(t)+f(t),
u(0)=u
o
, α∈(0,1), and 0≤ε, δ<α under the assumption that A is the generator of a bounded C
o
-semigroup. The continuation of our solution in some different cases for α, ε and δ is discussed, as well as the importance of the obtained results is specified. 相似文献
3.
S. H. Saker 《Nonlinear Oscillations》2011,13(3):407-428
Our aim is to establish some sufficient conditions for the oscillation of the second-order quasilinear neutral functional
dynamic equation
( p(t)( [ y(t) + r(t)y( t(t) ) ]D )g )D + f( t,y( d(t) ) = 0, t ? [ t0,¥ )\mathbbT, {\left( {p(t){{\left( {{{\left[ {y(t) + r(t)y\left( {\tau (t)} \right)} \right]}^\Delta }} \right)}^\gamma }} \right)^\Delta } + f\left( {t,y\left( {\delta (t)} \right)} \right. = 0,\quad t \in {\left[ {{t_0},\infty } \right)_\mathbb{T}}, 相似文献
4.
We establish the existence and uniqueness results over the semi-infinite interval [0,∞) for a class of nonlinear third order
ordinary differential equations of the form
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