共查询到20条相似文献,搜索用时 31 毫秒
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Chelo Ferreira José L. López Ester Pérez Sinusía 《Studies in Applied Mathematics》2023,150(1):254-276
We consider the highly oscillatory integral for large positive values of w, , K and p positive integers with , and an entire function. The standard saddle point method is complicated and we use here a simplified version of this method introduced by López et al. We derive an asymptotic approximation of this integral when for general values of K and p in terms of elementary functions, and determine the Stokes lines. For , the asymptotic behavior of this integral may be classified in four different regions according to the even/odd character of the couple of parameters K and p; the special case requires a separate analysis. As an important application, we consider the family of canonical catastrophe integrals for large values of one of its variables, say , and bounded values of the remaining ones. This family of integrals may be written in the form for appropriate values of the parameters w, θ and the function . Then, we derive an asymptotic approximation of the family of canonical catastrophe integrals for large . The approximations are accompanied by several numerical experiments. The asymptotic formulas presented here fill up a gap in the NIST Handbook of Mathematical Functions by Olver et al. 相似文献
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David J. Needham John C. Meyer John Billingham Catherine Drysdale 《Studies in Applied Mathematics》2023,150(4):963-995
In this paper, we consider the classical Riemann problem for a generalized Burgers equation, with a spatially dependent, nonlinear sound speed, with , which decays algebraically with increasing distance from a fixed spatial origin. When , this reduces to the classical Burgers equation. In this first part of a pair of papers, we focus attention on the large-time structure of the associated Riemann problem, and obtain its detailed structure, as , via the method of matched asymptotic coordinate expansions (this uses the classical method of matched asymptotic expansions, with the asymptotic parameters being the independent coordinates in the evolution problem; this approach is developed in detail in the monograph of Leach and Needham, as referenced in the text), over all parameter ranges. We identify a significant bifurcation in structure at . 相似文献
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We propose susceptible-infected-susceptible epidemic reaction–diffusion models with cognitive movement and nonlinear incidence in a spatially heterogeneous environment. The cognitive dispersal term takes either random diffusion or symmetric diffusion. Building upon the -estimates of positive solutions under , we state the asymptotic dynamics for , . The numerical results reveal spatial segregation of susceptible and infected populations: (a) the heterogeneous random diffusion can segregate the population and reduce the infection fraction significantly; (b) the segregation phenomenon disappears as the ratio approaches one from below; (c) the disease-free region strengthens the segregation induced by heterogeneous random diffusion; (d) the segregation governed by random diffusion is more sensitive to the incidence mechanism; (e) the distribution of steady states driven by symmetric diffusion is always similar to that by homogeneous diffusion. 相似文献
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We introduce a new family of multiple orthogonal polynomials satisfying orthogonality conditions with respect to two weights on the positive real line, with the gamma density and a density related to the exponential integral . We give explicit formulas for the type I functions and type II polynomials, their Mellin transform, Rodrigues formulas, hypergeometric series, and recurrence relations. We determine the asymptotic distribution of the (scaled) zeros of the type II multiple orthogonal polynomials and make a connection to random matrix theory. Finally, we also consider two related families of mixed-type multiple orthogonal polynomials. 相似文献
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Alessandro Columbu Silvia Frassu Giuseppe Viglialoro 《Studies in Applied Mathematics》2023,151(4):1349-1379
This paper deals with unbounded solutions to a class of chemotaxis systems. In particular, for a rather general attraction–repulsion model, with nonlinear productions, diffusion, sensitivities, and logistic term, we detect Lebesgue spaces where given unbounded solutions also blow up in the corresponding norms of those spaces; subsequently, estimates for the blow-up time are established. Finally, for a simplified version of the model, some blow-up criteria are proved. More precisely, we analyze a zero-flux chemotaxis system essentially described as (⋄) The problem is formulated in a bounded and smooth domain Ω of , with , for some , , , and with . A sufficiently regular initial data is also fixed. Under specific relations involving the above parameters, one of these always requiring some largeness conditions on ,
- (i) we prove that any given solution to (), blowing up at some finite time becomes also unbounded in -norm, for all ;
- (ii) we give lower bounds T (depending on ) of for the aforementioned solutions in some -norm, being ;
- (iii) whenever , we establish sufficient conditions on the parameters ensuring that for some u0 solutions to () effectively are unbounded at some finite time.
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This study concerns with the existence–uniqueness of local classical sonic-supersonic solution to a degenerate Cauchy–Goursat problem that arises in transonic phenomena. The flow is governed by 2-D steady isentropic Euler system with a polytropic van der Waals gas. The idea of characteristic decomposition has been used to convert the Euler system into a new system involving the angle variables . To overcome the parabolic degeneracy caused at the sonic curve, the partial hodograph transformation and a variety of dependent–independent variables have been introduced to transform the nonlinear system into a linear one with explicit singularity–regularity structure. The uniform convergence of the sequences has been discussed by employing the mathematical induction. Eventually, the inversion of the solution from partial hodograph plane to the original plane has been established. 相似文献
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The Riesz potential is known to be an important building block of many interactions, including Lennard-Jones–type potentials , that are widely used in molecular simulations. In this paper, we investigate analytically and numerically the minimizers among three-dimensional lattices of Riesz and Lennard-Jones energies. We discuss the minimality of the body-centered-cubic (BCC) lattice, face-centered-cubic (FCC) lattice, simple hexagonal (SH) lattices, and hexagonal close-packing (HCP) structure, globally and at fixed density. In the Riesz case, new evidence of the global minimality at fixed density of the BCC lattice is shown for and the HCP lattice is computed to have higher energy than the FCC (for ) and BCC (for ) lattices. In the Lennard-Jones case with exponents , the ground state among lattices is confirmed to be an FCC lattice whereas an HCP phase occurs once added to the investigated structures. Furthermore, phase transitions of type “FCC-SH” and “FCC-HCP-SH” (when the HCP lattice is added) as the inverse density V increases are observed for a large spectrum of exponents . In the SH phase, the variation of the ratio Δ between the interlayer distance d and the lattice parameter a is studied as V increases. In the critical region of exponents , the SH phase with an extreme value of the anisotropy parameter Δ dominates. If one limits oneself to rigid lattices, the BCC-FCC-HCP phase diagram is found. For , the BCC lattice is the only energy minimizer. Choosing , the FCC and SH latices become minimizers. 相似文献
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A Banach space X has property (K), whenever every weak* null sequence in the dual space admits a convex block subsequence so that as for every weakly null sequence in X; X has property if every weak* null sequence in admits a subsequence so that all of its subsequences are Cesàro convergent to 0 with respect to the Mackey topology. Both property and reflexivity (or even the Grothendieck property) imply property (K). In this paper, we propose natural ways for quantifying the aforementioned properties in the spirit of recent results concerning other familiar properties of Banach spaces. 相似文献
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Giovany M. Figueiredo Marcelo Montenegro Matheus F. Stapenhorst 《Mathematische Nachrichten》2023,296(10):4569-4609
We show the existence of a solution for an equation where the nonlinearity is logarithmically singular at the origin, namely, in with Dirichlet boundary condition. The function f has exponential growth, which can be subcritical or critical with respect to the Trudinger–Moser inequality. We study the energy functional corresponding to the perturbed equation , where is well defined at 0 and approximates . We show that has a critical point in , which converges to a legitimate nontrivial nonnegative solution of the original problem as . We also investigate the problem with replaced by , when the parameter is sufficiently large. 相似文献
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Ferenc Weisz 《Mathematische Nachrichten》2023,296(4):1687-1705
Let be a measurable function defined on and . In this paper, we generalize the Hardy–Littlewood maximal operator. In the definition, instead of cubes or balls, we take the supremum over all rectangles the side lengths of which are in a cone-like set defined by a given function ψ. Moreover, instead of the integral means, we consider the -means. Let and satisfy the log-Hülder condition and . Then, we prove that the maximal operator is bounded on if and is bounded from to the weak if . We generalize also the theorem about the Lebesgue points. 相似文献
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Gen Qi Xu 《Mathematische Nachrichten》2023,296(6):2626-2656
In this paper, we investigate a class of the linear evolution process with memory in Banach space by a different approach. Suppose that the linear evolution process is well posed, we introduce a family pair of bounded linear operators, , that is, called the resolvent family for the linear evolution process with memory, the is called the memory effect family. In this paper, we prove that the families and are exponentially bounded, and the family associate with an operator pair that is called generator of the resolvent family. Using , we derive associated differential equation with memory and representation of via L. These results give necessary conditions of the well-posed linear evolution process with memory. To apply the resolvent family to differential equation with memory, we present a generation theorem of the resolvent family under some restrictions on . The obtained results can be directly applied to linear delay differential equation, integro-differential equation and functional differential equations. 相似文献
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Roger Bielawski 《Mathematische Nachrichten》2023,296(1):122-129
We show that -invariant hypercomplex structures on (open subsets) of regular semisimple adjoint orbits in correspond to algebraic curves C of genus , equipped with a flat projection of degree k, and an antiholomorphic involution covering the antipodal map on . 相似文献
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Paulo Cesar Carrião Olímpio Hiroshi Miyagaki André Vicente 《Mathematische Nachrichten》2023,296(1):130-151
In this paper, we study the exponential decay of the energy associated to an initial value problem involving the wave equation on the hyperbolic space . The space is the unit disc of endowed with the Riemannian metric g given by , where and , if and , if . Making an appropriate change, the problem can be seen as a singular problem on the boundary of the open ball endowed with the euclidean metric. The proof is based on the multiplier techniques combined with the use of Hardy's inequality, in a version due to the Brezis–Marcus, which allows us to overcome the difficulty involving the singularities. 相似文献
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