1,721,261 research outputs found
Ordering properties of radial ground states and singular ground states of quasilinear elliptic equations
Full text linkIn this paper we discuss the ordering properties of positive radial solutions of the equation Δpu(x)+k|x|δuq-1(x)=0where x∈ Rn, n> p> 1 , k> 0 , δ> - p, q> p. We are interested both in regular ground states u (GS), defined and positive in the whole of Rn, and in singular ground states v (SGS), defined and positive in Rn { 0 } and such that lim |x|→v(x) = + ∞. A key role in this analysis is played by two bifurcation parameters pJL(δ) and pjl(δ) , such that pJL(δ) > p∗(δ) > pjl(δ) > p: pJL(δ) generalizes the classical Joseph–Lundgren exponent, and pjl(δ) its dual. We show that GS are well ordered, i.e. they cannot cross each other if and only if q≥ pJL(δ) ; this way we extend to the p> 1 case the result proved in Miyamoto (Nonlinear Differ Equ Appl 23(2):24, 2016), Miyamoto and Takahashi (Arch Math Basel 108(1):71–83, 2017) for the p≥ 2 case. Analogously we show that SGS are well ordered, if and only if q≤ pjl(δ) ; this latter result seems to be known just in the classical p= 2 and δ= 0 case, and also the expression of pjl(δ) has not appeared in literature previously
Periodic travelling waves for a fourth order nonlinear evolution equation
Full text linkIn this article we provide a travelling wave analysis for a fourth order non linear evolution equation. In particular we prove the existence of periodic travelling waves while we exclude the existence of solitary waves for proper values of the parameters. Moreover, we analyse the set of stationary solutions and provide a new proof of the existence of limit cycle for a related equation, that is, the Van der Pol equation
A qualitative description of microstructure formation and coarsening phenomena for an evolution equation
No full textWe provide a qualitative description of microstructure formation and coarsening phenomena for the solutions of a singularly perturbed fourth order evolution equation arising in the study of phase transitions. In particular we study stationary and traveling wave solutions and we construct a class of approximate solution which mimics the principle features of the dynamics. Finally we present several simulations in order to illustrate the results
Climate change and rapid ice melt: Suggestions from abrupt permafrost degradation and ice melting in an alpine ice cave
No full textAmong the different elements of the mountain cryosphere, ice caves still represent the lesser known part of it. Here we present a seven-year-long record of air and rock temperature in a cave of the southeastern European Alps. We demonstrate how the presence of a permanent ice deposit in the cave is not only related to the net cooling effect of the air circulation, as it is well known, but also to the occurrence of relict permafrost. Through a detailed representation of temperature patterns inside the cave, both air and rock data show how after a period of perennially subzero (cryotic) conditions in the rock, ongoing anthropogenic climate warming is responsible for permafrost degradation despite the cooling effect of the air circulation in the cave. Data support the important role of cryotic conditions in the rock in preserving a permanent ice cave deposit in the present climate, even once the possible relict permafrost inherited from the past disappears. A thickness of 29–44 m of permafrost, possibly formed during the Little Ice Age, has now almost completely disappeared. The present abrupt ice degradation observed in this cave is further exacerbated by positive feedbacks related to warmer air circulation in the cave system
Rock glaciers, protalus ramparts and pronival ramparts in the south-eastern Alps
No full textRock glaciers and protalus ramparts are characteristic landforms of the periglacial domain often used as markers for the occurrence of permafrost in mountain terrains. As such, relict rock glaciers can be used for paleoclimate reconstructions. We present here the first previously unreported rock glacier inventory of the south-eastern Alps (including the north-eastern-most region of Italy and Slovenia), interpreted from high resolution orthophotos and a high resolution digital terrain model interpolated from airborne laser scanning (LiDAR). We mapped 53 rock glaciers covering a total area of 3.45 km2. The majority of rock glaciers are classified as relict and distributed between 1708 and 1846 m a.s.l. with slope ranging between 19° and 27°. In addition to rock glaciers we observed 66 protalus (pronival) ramparts, having median elevation of 1913 m a.s.l. and covering 0.48 km2. More than half of the inventoried protalus ramparts are located in the more maritime area of the Alps with higher precipitation compared to the location of rock glaciers. Using paleoclimate reconstruction based on the 1981–2010 climatological record of the area, we infer that the rock glaciers formed during one of the dry and cold periods of the late Pleistocene and early Holocene. Possible evolution of the active pronival forms observed in the most maritime area of this alpine sector is also discussed
Dynamics of fermentation models for the production of dry and sweet wine
No full textIn this work we consider two classical mathematical models of wine fermentation. The first model describes the wine-making process that is used to produce dry wine. The second model is obtained by introducing a term in the equation of the dynamics of the yeast. Thanks to this change it will be possible to inhibit the fermentation of the sugar and as a consequence a sweet wine will be obtained. We first prove the existence, uniqueness, positiveness and boundedness of solutions for both models. Then we pass to analyse the the long-time dynamics. For the second model we also provide estimates for the concentration of ethanol, nitrogen and sugar at the end of the process. Moreover, several numerical simulations are provided to support the theoretical results
An estimate concerning the difference between minimizer and boundary value in some polyconvex problems
Full text linkThis paper is concerned with regularity of minimizers of integral functionals with polyconvex potentials. In particular we obtain bounds on the difference |u−u∗|∞ for minimizers u:Ω⊂R3→R3 of problem min∫Ωf(x,Dv(x))dx,v∈u∗+W01,p(Ω,R3)
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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