Bounded Minimisers of Double Phase Variational Integrals

Archive for Rational Mechanics and Analysis - Bounded minimisers of the functional $$w \mapsto \int (|Dw|^p+a(x)|Dw|^q)\,{\rm d}x,$$ where $${0 \leqq a(\cdot) \in C^{0, \alpha}}$$ and $${1 <...     

Topological Conjugation Classes of Tightly Transitive Subgroups of $$\text {Homeo}_{+}(\mathbb {S}^1)$$ Homeo + ( S 1 )

Journal of Dynamics and Differential Equations - Let $$\text {Homeo}_{+}(\mathbb {S}^1)$$ denote the group of orientation preserving homeomorphisms of the circle $$\mathbb {S}^1$$ . A subgroup G of...     

Boundary-layer development beyond a critical value

Meccanica - Two initial-value problems are considered involving a parameter $$\alpha $$ , the corresponding steady states have a critical value at $$\alpha =\alpha _c<0$$ with steady state...     

Full Measure Reducibility for Generic One-parameter Family of Quasi-periodic Linear Systems

Let be the set of m × m matrices A(λ) depending analytically on a parameter λ in a closed interval . Consider one-parameter families of quasi-periodic linear differential equations: , where is analytic and sufficiently small. We prove that there is an open and dense set in , such that for each the equation can be reduced to an equation with constant coefficients by a quasi-periodic linear transformation for almost all in Lebesgue measure sense provided that g is sufficiently small. The result gives an affirmative answer to a conjecture of Eliasson (In: Proceeding of Symposia in Pure Mathematics). Dedicated to Professor Zhifen Zhang on the occasion of her 80th birthday     

Lump-type solution and breather lump–kink interaction phenomena to a ($$\mathbf{{3{\varvec{+}}1}}$$3+1)-dimensional GBK equation based on trilinear form

Nonlinear Dynamics - In this paper, the multivariate trilinear operators in the ($$3+1$$)-dimensional space are applied to a ($$3+1$$)-dimensional GBK equation. The resulting trilinear form is used...     

Self-similar approximants of the permeability in heterogeneous porous media from moment equation expansions

We use a mathematical technique, the self-similar functional renormalization, to construct formulas for the average conductivity that apply for large heterogeneity, based on perturbative expansions in powers of a small parameter, usually the log-variance of the local conductivity. Using perturbation expansions up to third order and fourth order in obtained from the moment equation approach, we construct the general functional dependence of the scalar hydraulic conductivity in the regime where is of order 1 and larger than 1. Comparison with available numerical simulations show that the proposed method provides reasonable improvements over available expansions.     

Robust $$H_{\infty }$$ H ∞ adaptive output feedback sliding mode control for interval type-2 fuzzy fractional-order systems with actuator faults

Nonlinear Dynamics - This paper addresses the $$H_{\infty }$$ adaptive output feedback sliding mode fault-tolerant control problem for uncertain nonlinear fractional-order $$\hbox {systems}$$...     

Effects of Hydrogen-Enrichment on Flame-Holding of Natural Gas Jet Flames in Crossflow at Elevated Temperature and Pressure

Flow, Turbulence and Combustion - The effect of hydrogen ( $$\mathrm {H}_{\mathrm {2}}$$ ) enrichment on the flame-holding characteristics of two natural gas jet flames in crossflow is investigated...     

Vector potential–vorticity relationship for the Stokes flows: application to the Stokes eigenmodes in 2D/3D closed domain

The unsteady dynamics of the Stokes flows, where , is shown to verify the vector potential–vorticity ( ) correlation , where the field is the pressure-gradient vector potential defined by . This correlation is analyzed for the Stokes eigenmodes, , subjected to no-slip boundary conditions on any two-dimensional (2D) closed contour or three-dimensional (3D) surface. It is established that an asymptotic linear relationship appears, verified in the core part of the domain, between the vector potential and vorticity, , where is a constant offset field, possibly zero.     

Stable and oscillating solitons of $$\pmb {\mathcal {PT}}$$ -symmetric couplers with gain and loss in fractional dimension

Nonlinear Dynamics - Families of coupled solitons of $$\mathcal {PT}$$ -symmetric physical models with gain and loss in fractional dimension and in settings with and without cross-interactions...     

The Steady Motion of a Navier–Stokes Liquid Around a Rigid Body

Let be a body moving by prescribed rigid motion in a Navier–Stokes liquid that fills the whole space and is subject to given boundary conditions and body force. Under the assumptions that, with respect to a frame , attached to , these data are time independent, and that their magnitude is not “too large”, we show the existence of one and only one corresponding steady motion of , with respect to , such that the velocity field, at the generic point x in space, decays like |x|⁻¹. These solutions are “physically reasonable” in the sense of FINN [10]. In particular, they are unique and satisfy the energy equation. Among other things, this result is relevant in engineering applications involving orientation of particles in viscous liquid [14].     

Long-Term Redistribution of Residual Gas Due to Non-convective Transport in the Aqueous Phase

Transport in Porous Media - Geological CO $$_2$$ sequestration is an effective approach to mitigate greenhouse gas emissions by permanently trapping CO $$_2$$ in the subsurface. A large portion of...     

External stability of Caputo fractional-order nonlinear control systems: advances in the Lyapunov function method

Nonlinear Dynamics - Nonlinear behavior of bubbles, and most importantly $$\frac{1}{2}$$ -order subharmonics (SH), are used to increase the contrast-to-tissue ratio (CTR) in diagnostic ultrasound...     

The integrability conditions and solutions of nonautonomous Hirota equation

Nonlinear Dynamics - In this paper, we prove an elementary lemma which estimates fractional derivatives of Lyapunov function in the sense Caputo when $$\alpha \in (0,1)$$ . Moreover, by using this...     

Coexistence of singular cycles in a new kind of 3D non-smooth systems with two discontinuous boundaries

Nonlinear Dynamics - The aim here is to study complex dynamical behavior in a new kind of non-smooth systems with two discontinuous boundaries in space $$\mathbb {R}^3$$ . This paper provides an...     

Unexpected Behavior of Nonautonomous Linear Dynamical Systems in Two Dimensions

We show two examples of systems in with such that |Z_t| is strictly decreasing in time for any n but as .     

An Analytical Model for Flow of Seawater Adjacent to an Igneous Wall

Transport in Porous Media - We develop an analytical model describing the flow of NaCl– $$\hbox {H}_2\hbox {O}$$ in a saturated porous medium adjacent to a hot vertical wall and apply the...     

Existence of n-cycles and border-collision bifurcations in piecewise-linear continuous maps with applications to recurrent neural networks

The purpose of these comments is to correct the derivation of perturbed first-order $$\varepsilon ^{1}$$-equation, for modeling the acoustic scattering waves from a composite beam. We have introduced the correct solutions of displacements and potential functions in the first and second orders, although the mathematical treatment in solving the coupled nonlinear PDEs in the time-space domain looks good. So, the revised equation and the correct second-order $$\varepsilon ^2$$ equation are presented in this note.     

A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains

Archive for Rational Mechanics and Analysis - We investigate quantitative properties of the nonnegative solutions $${u(t,x)\geq 0}$$ to the nonlinear fractional diffusion equation, $${\partial_t u...     

Kinetic Limit for Wave Propagation in a Random Medium

We study crystal dynamics in the harmonic approximation. The atomic masses are weakly disordered, in the sense that their deviation from uniformity is of the order . The dispersion relation is assumed to be a Morse function and to suppress crossed recollisions. We then prove that in the limit , the disorder-averaged Wigner function on the kinetic scale, time and space of order , is governed by a linear Boltzmann equation.