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Global existence and analyticity of mild solutions for the stochastic Navier–Stokes–Coriolis equations in Besov spaces
Publication date: April 2020Source: Nonlinear Analysis: Real World Applications, Volume 52Author(s): Weihua WangAbstractConsider the stochastic Navier–Stokes–Coriolis equation in R3 driven by an additive white noise, we establish the unique existence and spatial analyticity of global mild solution even when initial data is essentially arbitrarily large and even when stochastic external force is also large provided that the speed of the rotation is fast enough. The proof is based on the Picard contraction principle and a priori estimates to the stochastic parabolic equation. (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - October 11, 2019 Category: Research Source Type: research

On the number of limit cycles for a class of piecewise smooth Hamiltonian systems with discontinuous perturbations
Publication date: April 2020Source: Nonlinear Analysis: Real World Applications, Volume 52Author(s): Jihua Yang, Erli ZhangAbstractBy analyzing the corresponding Picard–Fuchs equations, we obtain an upper bound of the number of limit cycles for a class of piecewise smooth Hamiltonian systems when they are perturbed inside discontinuous polynomials of degree n. Finally, we present an example to illustrate an application of the theoretical results. (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - October 10, 2019 Category: Research Source Type: research

Dynamics and steady-state analysis of an unstirred chemostat model with internal storage and toxin mortality
This study proposes and analyzes a reaction–diffusion system describing the competition of two species for a single limiting nutrient that is stored internally in an unstirred chemostat, in which each species also produces a toxin that increases the mortality of its competitors. The possibility of coexistence and bistability for the model system is studied by the theory of uniform persistence and topological degree theory in cones, respectively. More precisely, the sharp a priori estimates for nonnegative solutions of the system are first established, which assure that all of nonnegative solutions belong to a special con...
Source: Nonlinear Analysis: Real World Applications - October 2, 2019 Category: Research Source Type: research

Pointwise stability of shock wave for 2D anisotropic viscous conservation laws with large perturbation
Publication date: April 2020Source: Nonlinear Analysis: Real World Applications, Volume 52Author(s): Kaiqiang Li, Weike WangAbstractIn this paper, we are interested in the well-posedness of solutions for anisotropic scalar conservation law with large perturbation around the planar shock wave in two dimensional space. It is shown that the Cauchy problem admits a global classical solution by using the classical energy estimates and contraction property, while the initial perturbation is bounded in given space, where we used some new inequalities for anisotropic terms which was imposed in Lemma 2.7. Moreover, we obtain the po...
Source: Nonlinear Analysis: Real World Applications - October 1, 2019 Category: Research Source Type: research

Blow-up result and energy decay rates for binary mixtures of solids with nonlinear damping and source terms
Publication date: April 2020Source: Nonlinear Analysis: Real World Applications, Volume 52Author(s): M.L. Santos, M.M. Freitas, A.J.A. RamosAbstractIn this paper we study the long-time behavior of binary mixture problem of solids, focusing on the interplay between nonlinear damping and source terms. By employing nonlinear semigroups and the theory of monotone operators, we obtain several results on the existence of local and global weak solutions, and uniqueness of weak solutions. Moreover, we prove that every weak solution to our system blows up in finite time, provided the initial energy is negative and the sources are m...
Source: Nonlinear Analysis: Real World Applications - September 28, 2019 Category: Research Source Type: research

Persistence properties and asymptotic behavior for a two-component b-family system with high order nonlinearity
Publication date: April 2020Source: Nonlinear Analysis: Real World Applications, Volume 52Author(s): Ngul Suan Lian, Kai YanAbstractThis paper is devoted to the study of persistence properties and asymptotic behavior for a two-component b-family system with high order nonlinearity. We prove that both the density and momentum components of the corresponding solutions with initial compact support will retain the property of being compactly supported throughout its evolution. Moreover, we investigate the asymptotic behaviors of the solutions at infinity within its lifespan when the initial data decay exponentially and algebra...
Source: Nonlinear Analysis: Real World Applications - September 28, 2019 Category: Research Source Type: research

Concentration of mass in the pressureless limit of the Euler equations of one-dimensional compressible fluid flow
Publication date: April 2020Source: Nonlinear Analysis: Real World Applications, Volume 52Author(s): Shouqiong Sheng, Zhiqiang ShaoAbstractIn this paper, we study the limiting behavior of Riemann solutions to the Euler equations of one-dimensional compressible fluid flow as γ tends to one. We show that the limit solution forms the delta wave to the pressureless Euler system of one-dimensional compressible fluid flow in the distribution sense. Some numerical results exhibiting the phenomena of concentration are also presented. (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - September 28, 2019 Category: Research Source Type: research

Expansion of gas by turning a sharp corner into vacuum for 2-D pseudo-steady compressible magnetohydrodynamics system
Publication date: April 2020Source: Nonlinear Analysis: Real World Applications, Volume 52Author(s): Jianjun Chen, Gan Yin, Shouke YouAbstractThis paper is concerned with the process of a gas expanding into vacuum by turning around a sharp corner for 2-D pseudo-steady compressible magnetohydrodynamics system. This problem actually can be interpreted as interaction of a centered wave and a planar rarefaction wave. As the gas touches the corner and starts expanding into the vacuum around the sharp corner, a centered wave and a planar rarefaction wave appear. In the estimates of solution, we utilize the characteristic analysi...
Source: Nonlinear Analysis: Real World Applications - September 25, 2019 Category: Research Source Type: research

Positive periodic solutions for Lotka–Volterra systems with a general attack rate
Publication date: April 2020Source: Nonlinear Analysis: Real World Applications, Volume 52Author(s): Cristina Lois-Prados, Radu PrecupAbstractThe paper deals with a non-autonomous Lotka–Volterra type system, which in particular may include logistic growth of the prey population and hunting cooperation between predators. We focus on the existence of positive periodic solutions by using an operator approach based on the Krasnosel’skii homotopy expansion theorem. We give sufficient conditions in order that the localized periodic solution does not reduce to a steady state. Particularly, two typical expressions for the func...
Source: Nonlinear Analysis: Real World Applications - September 14, 2019 Category: Research Source Type: research

Editorial Board
Publication date: February 2020Source: Nonlinear Analysis: Real World Applications, Volume 51Author(s): (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - September 11, 2019 Category: Research Source Type: research

Introducing article numbering to Nonlinear Analysis: Real World Applications
Publication date: February 2020Source: Nonlinear Analysis: Real World Applications, Volume 51Author(s): Darren Sugrue (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - September 11, 2019 Category: Research Source Type: research

Finite-time blow-up in a two-dimensional Keller–Segel system with an environmental dependent logistic source
Publication date: April 2020Source: Nonlinear Analysis: Real World Applications, Volume 52Author(s): Mario FuestAbstractThe Neumann initial–boundary problem for the chemotaxis system (⋆)ut=Δu−∇⋅(u∇v)+κ(|x|)u−μ(|x|)up,0=Δv−m(t)|Ω|+u,m(t)≔∫Ωu(⋅,t)is studied in a ball Ω=BR(0)⊂R2, R>0 for p≥1 and sufficiently smooth functions κ,μ:[0,R]→[0,∞).We prove that whenever μ′,−κ′≥0 as well as μ(s)≤μ1s2p−2 for all s∈[0,R] and some μ1>0 then for all m0>8π there exists u0∈C0(Ω¯) with ∫Ωu0=m0 and a solution (u,v) to (⋆) with initial datum u0 blowing up in finite time. If i...
Source: Nonlinear Analysis: Real World Applications - September 5, 2019 Category: Research Source Type: research

L3-solutions for the stationary Navier–Stokes equations in the exterior of a rotating obstacle
Publication date: April 2020Source: Nonlinear Analysis: Real World Applications, Volume 52Author(s): Dugyu KimAbstractConsider the stationary motion of an incompressible Navier–Stokes fluid around a rotating body R3∖Ω which is also moving in the direction of the axis of rotation with nonzero constant velocity −ke1. We assume that the angular velocity ω=|ω|e1 is also constant and the external force is given by f=divF. Then the motion is described by a variant of the stationary Navier–Stokes equations with the velocity ke1 at infinity. Our main result is the existence of at least one solution u satisfying u−ke1...
Source: Nonlinear Analysis: Real World Applications - September 2, 2019 Category: Research Source Type: research

The impact of time delay in a tumor model
Publication date: February 2020Source: Nonlinear Analysis: Real World Applications, Volume 51Author(s): Xinyue Evelyn Zhao, Bei HuAbstractIn this paper we consider a free boundary tumor growth model with a time delay in cell proliferation and study how time delay affects the stability and the size of the tumor. The model is a coupled system of an elliptic equation, a parabolic equation and an ordinary differential equation. It incorporates the cell location under the presence of time delay, with the tumor boundary as a free boundary. A parameter μ in the model is proportional to the “aggressiveness” of the tumor. It i...
Source: Nonlinear Analysis: Real World Applications - August 30, 2019 Category: Research Source Type: research

Strategies for the existence of spatial patterns in predator–prey communities generated by cross-diffusion
Publication date: February 2020Source: Nonlinear Analysis: Real World Applications, Volume 51Author(s): Swati Mishra, Ranjit Kumar UpadhyayAbstractFear of predators is an important drive for predator–prey interactions, which increases survival probability but cost the overall population size of the prey. In this paper, we have extended our previous work spatiotemporal dynamics of predator–prey interactions with fear effect by introducing the cross-diffusion. The conditions for cross-diffusion-driven instability are obtained using the linear stability analysis. The standard multiple scale analysis is used to derive the ...
Source: Nonlinear Analysis: Real World Applications - August 30, 2019 Category: Research Source Type: research