Results 11 to 20 of about 1,240,454 (293)
Optimal control for a two-sidedly degenerate aggregation equation
Nonlinear Analysis, 2023 In this paper, we are concerned with the study of the mathematical analysis for an optimal control of a nonlocal degenerate aggregation model. This model describes the aggregation of organisms such as pedestrian movements, chemotaxis, animal swarming ...
Mostafa Bendahmane +4 more
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Saturated Fronts in Crowds Dynamics
Advanced Nonlinear Studies, 2021 We consider a degenerate scalar parabolic equation, in one spatial dimension, of flux-saturated type. The equation also contains a convective term. We study the existence and regularity of traveling-wave solutions; in particular we show that they can be ...
Campos Juan +2 more
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Demonstratio Mathematica, 2021 In this work, we develop and analyze an explicit finite volume scheme for a one-dimensional nonlinear, degenerate, convection–diffusion equation having application in petroleum reservoir.
Mostefai Mohamed Lamine +2 more
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Traveling Waves in Degenerate Diffusion Equations
Communications in Mathematical Research, 2023 Summary: In this survey, we present a literature review on the study of traveling waves in degenerate diffusion equations by illustrating the interesting and singular wave behavior caused by degeneracy. The main results on wave existence and stability are presented for the typical degenerate equations, including porous medium equations, flux limited ...
Xu, Tianyuan, Yin, Jingxue
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Finite element approximation of a nonlinear cross-diffusion population model [PDF]
, 2003 We consider a fully discrete finite element approximation of the nonlinear cross-diffusion population model: Find u i, the population of the ith species, i = 1 and 2, such that ∂ui ∂t −Δ [ ci ui + ai u2i + ui uj] − bi ∇.
John W. Barrett +6 more
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Bulletin of Mathematical Sciences, 2023 A no-flux initial-boundary value problem for the cross-diffusion system ut = Δ(uϕ(v)),vt = Δv − uv is considered in smoothly bounded domains [Formula: see text] with [Formula: see text].
Michael Winkler
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A Note on the Degenerate Morse Inequalities [PDF]
, 2000 In this paper we give an analytic proof of the degenerate Morse inequalities in the spirit of E. Witten. The max-min methods are used to estimate the number of ‘small’ eigenvalues of Witten’s deformed Laplacian.
Jianwei, Zhou
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Dynamics of an impact oscillator near a degenerate graze [PDF]
, 2010 We give a complete analysis of low-velocity dynamics close to grazingfor a generic one degree of freedom impact oscillator. This includes nondegenerate (quadratic) grazing and minimallydegenerate (cubic) grazing, corresponding respectively to ...
D R J Chillingworth +2 more
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Doubly degenerate diffuse interface models of anisotropic surface diffusion [PDF]
Mathematical Methods in the Applied Sciences, 2020 We extend the doubly degenerate Cahn–Hilliard (DDCH) models for isotropic surface diffusion, which yield more accurate approximations than classical degenerate Cahn–Hilliard (DCH) models, to the anisotropic case. We consider both weak and strong anisotropies and demonstrate the capabilities of the approach for these cases numerically.
Salvalaglio, Marco +3 more
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Advanced Nonlinear Studies, 2022 The chemotaxis–Stokes system nt+u⋅∇n=∇⋅(D(n)∇n)−∇⋅(nS(x,n,c)⋅∇c),ct+u⋅∇c=Δc−nc,ut=Δu+∇P+n∇Φ,∇⋅u=0,\left\{\begin{array}{l}{n}_{t}+u\cdot \nabla n=\nabla \cdot (D\left(n)\nabla n)-\nabla \cdot (nS\left(x,n,c)\cdot \nabla c),\\ {c}_{t}+u\cdot \nabla c ...
Winkler Michael
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