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A generalized Duffing equation with the Coulomb’s friction law and Signorini–type contact conditions
This work provides mathematical and numerical analyses for a spring–mass system, in which Signorini–type contact conditions and Coulomb’s friction law with thermal effects are taken into consideration. The motion of a mass attached to a viscoelastic (Kelvin–Voigt type) nonlinear spring is described by a generalized Duffing equation. Signorini contact conditions are understood as extended complementarity conditions (CCs), where convolution is incorporated, allowing to consider thermal aspects of an obstacle. We prove the existence of global weak solutions for the highly nonlinear differential equation system with all the conditions, based on the regularized differential equation and the normal compliance condition with the standard mollifier. In addition, we investigate what side effects produce higher singularities of contact forces in dynamic contact problems, which is also supported by numerical evidences. Numerical schemes are proposed and then several groups of data are selected for the display of our numerical simulations. 相似文献
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Plane quartic curves given by equations of the form y
2=P(x) with polynomials P of degree 4 represent singular models of elliptic curves which are directly related to elliptic integrals in the form studied
by Euler and for which he developed his famous addition formulas. For cubic curves, the well-known secant and tangent construction
establishes an immediate connection of addition formulas for the corresponding elliptic integrals with the structure of an
algebraic group. The situation for quartic curves is considerably more complicated due to the presence of the singularity.
We present a geometric construction, similar in spirit to the secant method for cubic curves, which defines an addition law
on a quartic elliptic curve given by rational functions. Furthermore, we show how this addition on the curve itself corresponds
to the addition in the (generalized) Jacobian variety of the curve, and we show how any addition formula for elliptic integrals
of the form ò(1/?{P(x)}) dx\int (1/\sqrt{P(x)})\,\mathrm{d}x with a quartic polynomial P can be derived directly from this addition law. 相似文献
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In this paper we consider a diffusion system with the Belousov–Zhabotinskii (BZ for short) chemical reaction. Following Brazhnik and Tyson [4] and Pérez-Muñuzuri et al. [45], who predicted V-shaped fronts theoretically and discovered V-shaped fronts by experiments respectively, we give a rigorous mathematical proof of their results. We establish the existence of V-shaped traveling fronts in by constructing a proper supersolution and a subsolution. Furthermore, we establish the stability of the V-shaped front in . 相似文献