共查询到20条相似文献,搜索用时 109 毫秒
1.
Stefano Bianchini Camillo De Lellis Roger Robyr 《Archive for Rational Mechanics and Analysis》2011,200(3):1003-1021
In this paper we study the regularity of viscosity solutions to the following Hamilton–Jacobi equations In particular, under the assumption that the Hamiltonian \({H\in C^2({\mathbb R}^n)}\) is uniformly convex, we prove that D x u and ? t u belong to the class SBV loc (Ω).
相似文献
$\partial_{t}u+H(D_{x}u)=0\quad\hbox{in }\Omega\subset{\mathbb R}\times{\mathbb R}^{n}.$
2.
Chung Fang 《Continuum Mechanics and Thermodynamics》2016,28(4):1049-1069
The turbulent flow characteristics of an isothermal dry granular dense matter with incompressible grains are investigated by the proposed first-order k–\({\varepsilon}\) turbulence closure model. Reynolds-filter process is applied to obtain the balance equations of the mean fields with two kinematic equations describing the time evolutions of the turbulent kinetic energy and dissipation. The first and second laws of thermodynamics are used to derive the equilibrium closure relations satisfying turbulence realizability conditions, with the dynamic responses postulated by a quasi-linear theory. The established closure model is applied to analyses of a gravity-driven stationary flow down an inclined moving plane. While the mean velocity decreases monotonically from its value on the moving plane toward the free surface, the mean porosity increases exponentially; the turbulent kinetic energy and dissipation evolve, respectively, from their minimum and maximum values on the plane toward their maximum and minimum values on the free surface. The evaluated mean velocity and porosity correspond to the experimental outcomes, while the turbulent dissipation distribution demonstrates a similarity to that of Newtonian fluids in turbulent shear flows. When compared to the zero-order model, the turbulent eddy evolution tends to enhance the transfer of the turbulent kinetic energy and plane shearing across the flow layer, resulting in more intensive turbulent fluctuation in the upper part of the flow. Solid boundary as energy source and sink of the turbulent kinetic energy becomes more apparent in the established first-order model. 相似文献
3.
The Vlasov–Poisson–Boltzmann System governs the time evolution of the distribution function for dilute charged particles in
the presence of a self-consistent electric potential force through the Poisson equation. In this paper, we are concerned with
the rate of convergence of solutions to equilibrium for this system over
\mathbb R3{\mathbb R^3}. It is shown that the electric field, which is indeed responsible for the lowest-order part in the energy space, reduces
the speed of convergence, hence the dispersion of this system over the full space is slower than that of the Boltzmann equation
without forces; the exact L
2-rate for the former is (1 + t)−1/4 while it is (1 + t)−3/4 for the latter. For the proof, in the linearized case with a given non-homogeneous source, Fourier analysis is employed to
obtain time-decay properties of the solution operator. In the nonlinear case, the combination of the linearized results and
the nonlinear energy estimates with the help of the proper Lyapunov-type inequalities leads to the optimal time-decay rate
of perturbed solutions under some conditions on initial data. 相似文献
4.
Nonlinear Dynamics - In this paper, a new methodology is proposed to derive the high-order approximations of motions near them in three cases, i.e., the mass ratio is greater than, smaller than and... 相似文献
5.
Juhi Jang 《Archive for Rational Mechanics and Analysis》2008,188(2):265-307
The dynamics of gaseous stars can be described by the Euler–Poisson system. Inspired by Rein’s stability result for , we prove the nonlinear instability of steady states for the adiabatic exponent under spherically symmetric and isentropic motion. 相似文献
6.
Nonlinear Dynamics - In this paper, some novel lump solutions and interaction phenomenon between lump and kink M-soliton are investigated. Firstly, we study the evolution and degeneration behaviour... 相似文献
7.
Nonlinear Dynamics - The chimera state, exhibiting a hybrid state of coexisting coherent and incoherent behaviors, has become a fast growing field in the past decade. In this paper, we investigate... 相似文献
8.
Nonlinear Dynamics - The fusion estimation issue of sensor networks is investigated for nonlinear time-varying systems with energy constraints, time delays as well as packet loss. For the addressed... 相似文献
9.
Vincenzo Ambrosio Hichem Hajaiej 《Journal of Dynamics and Differential Equations》2018,30(3):1119-1143
This paper is concerned with the following fractional Schrödinger equation where \(s\in (0,1),N> 2s, (-\Delta )^{s}\) is the fractional Laplacian, k is a bounded positive function, \(h\in L^{2}(\mathbb {R}^{N}), h\not \equiv 0\) is nonnegative and f is either asymptotically linear or superlinear at infinity. By using the s-harmonic extension technique and suitable variational methods, we prove the existence of at least two positive solutions for the problem under consideration, provided that \(|h|_{2}\) is sufficiently small.
相似文献
$$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s} u+u= k(x)f(u)+h(x) \text{ in } \mathbb {R}^{N}\\ u\in H^{s}(\mathbb {R}^{N}), \, u>0 \text{ in } \mathbb {R}^{N}, \end{array} \right. \end{aligned}$$
10.
Nonlinear Dynamics - In this paper, we investigate the event-triggered $$H_\infty $$ controller synthesis issue for vehicle suspension systems with linear fractional uncertainties. An active... 相似文献
11.
Nonlinear Dynamics - Fission and fusion are important phenomena, which have been observed experimentally in many physical areas. In this paper, we study the above two phenomena in the ( $$2+1$$... 相似文献
12.
Based on the mass transfer theory, a new mass transfer model of ion-exchange process on zeolite under liquid film diffusion
control is established, and the kinetic curves and the mass transfer coefficients of –K+ ion-exchange under different conditions were systemically determined using the shallow-bed experimental method. The results
showed that the –K+ ion-exchange rates and transfer coefficients are directly proportional to solution flow rate and temperature, and inversely
proportional to solution viscosity and the size of zeolite granules. It also showed that the transfer coefficient is not influenced
by the ion concentrations. For a large ranges of operational conditions including temperatures (10 − 75°C), flow rates (0.031 m s−1 −0.26 m s−1), liquid viscosities (1.002 × 10−3 N s m−2 − 4.44 × 10−3 N s m−2), and zeolite granular sizes (0.2 − 1.45 mm), the average mass transfer coefficients calculated by the model agree with the
experimental results very well. 相似文献
13.
Nonlinear Dynamics - In this work, the $$(2+1)$$ -dimensional extended Kadomtsev–Petviashvili equation, which models the surface waves and internal waves in straits or channels, is... 相似文献
14.
Nonlinear Dynamics - In this paper, we study the $$(2 + 1)$$ -dimensional variable-coefficient Kadomtsev–Petviashvili equation, which has certain applications in fluids and plasmas. Via the... 相似文献
15.
Nonlinear Dynamics - Based on the N-soliton solutions of the $$(2+1)$$ -dimensional Sawada–Kotera equation, the collisions among lump waves, line waves, and breather waves are studied in this... 相似文献
16.
We prove global well-posedness for instationary Navier–Stokes equations with initial data in Besov space \({B^{0}_{n,\infty}(\Omega)}\) in whole and half space, and bounded domains of \({{\mathbb R}^{n}}\), \({n \geq 3}\). To this end, we prove maximal \({L^{\infty}_{\gamma}}\) -regularity of the sectorial operators in some Banach spaces and, in particular, maximal \({L^{\infty}_{\gamma}}\) -regularity of the Stokes operator in little Nikolskii spaces \({b^{s}_{q,\infty}(\Omega)}\), \({s \in (-1, 2)}\), which are of independent significance. Then, based on the maximal regularity results and \({b^{s_{1}}_{q_{1},\infty}-B^{s_{2}}_{q_{2,1}}}\) estimates of the Stokes semigroups, we prove global well-posedness for Navier–Stokes equations under smallness condition on \({\|u_{0}\|_{B^{0}_{n,\infty}(\Omega)}}\) via a fixed point argument using Banach fixed point theorem. 相似文献
17.
Kazuyuki Tsuda 《Journal of Mathematical Fluid Mechanics》2016,18(1):157-185
The compressible Navier–Stokes–Korteweg system is considered on \({\mathbb{R}^3}\) when the external force is periodic in the time variable. The existence of a time periodic solution is proved for a sufficiently small external force by using the time-T-map related to the linearized problem around the motionless state with constant density and absolute temperature. The spectral properties of the time-T-map is investigated by a potential theoretic method and an energy method in some weighted spaces. The stability of the time periodic solution is proved for sufficiently small initial perturbations. It is also shown that the \({L^\infty}\) norm of the perturbation decays as time goes to infinity. 相似文献
18.
Nonlinear Dynamics - In this paper, the finite-time $${\mathcal {H}}_\infty $$ control problem of nonlinear parabolic partial differential equation (PDE) systems with parametric uncertainties is... 相似文献
19.
Nonlinear Dynamics - This paper is devoted to weighted $${\mathcal {H}}_{\infty }$$ consensus design for continuous-time/discrete-time stochastic multi-agent systems with average dwell time (ADT)... 相似文献
20.
Nonlinear Dynamics - This paper presents a robust sampled-data $${H_\infty }$$ control scheme for vibration attenuation of offshore platforms subject to irregular wave forces and actuator... 相似文献