Results 21 to 30 of about 2,783 (131)
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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On non-resistive limit of 1D MHD equations with no vacuum at infinity
Advances in Nonlinear Analysis, 2021 In this paper, the Cauchy problem for the one-dimensional compressible isentropic magnetohydrodynamic (MHD) equations with no vacuum at infinity is considered, but the initial vacuum can be permitted inside the region. By deriving a priori ν (resistivity
Li Zilai, Wang Huaqiao, Ye Yulin
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Journal of Function Spaces, Volume 9, Issue 1, Page 17-40, 2011., 2011 We prove a homogenization result for monotone operators by using the method of multiscale convergence. More precisely, we study the asymptotic behavior as ε → 0 of the solutions uε of the nonlinear equation divaε(x, ∇uε) = divbε, where both aε and bε oscillate rapidly on several microscopic scales and aε satisfies certain continuity, monotonicity and
Andreas Almqvist +4 more
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Travelling wave solutions to some PDEs of mathematical physics
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 21, Page 1105-1120, 2004., 2004 Nonlinear operations such as multiplication of distributions are not allowed in the classical theory of distributions. As a result, some ambiguities arise when we want to solve nonlinear partial differential equations such as differential equations of elasticity and multifluid flows, or some new cosmological models such as signature changing space ...
Kourosh Nozari, Ghasem Alizadeh Afrouzi
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Symmetry group analysis and invariant solutions of hydrodynamic‐type systems
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 10, Page 487-534, 2004., 2004 We study point and higher symmetries of systems of the hydrodynamic type with and without an explicit dependence on t, x. We consider such systems which satisfy the existence conditions for an infinite‐dimensional group of hydrodynamic symmetries which implies linearizing transformations for these systems.
M. B. Sheftel
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A Beale-Kato-Madja breakdown criterion for an Oldroyd-B fluid in the creeping flow regime [PDF]
, 2007 We derive a criterion for the breakdown of solutions to the Oldroyd-B model in R3 in the limit of zero Reynolds number (creeping flow). If the initial stress field is in the Sobolev space Hm(R3), m > 5/2, then either a unique solution exists within this ...
R. Kupferman, C. Mangoubi, E. Titi
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Inviscid, zero Froude number limit of the viscous shallow water system
Open Mathematics, 2021 In this paper, we study the inviscid and zero Froude number limits of the viscous shallow water system. We prove that the limit system is represented by the incompressible Euler equations on the whole space.
Yang Jianwei, Liu Mengyu, Hao Huiyun
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Asymptotics for critical nonconvective type equations
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 8, Page 377-405, 2004., 2004 We study large‐time asymptotic behavior of solutions to the Cauchy problem for a model of nonlinear dissipative evolution equation. The linear part is a pseudodifferential operator and the nonlinearity is a cubic pseudodifferential operator defined by means of the inverse Fourier transformation and represented by bilinear and trilinear forms with ...
Nakao Hayashi +2 more
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Abstract and Applied Analysis, Volume 2004, Issue 10, Page 815-829, 2004., 2004 This paper deals with the initial‐boundary value problem for the system of motion equations of an incompressible viscoelastic medium with Jeffreys constitutive law in an arbitrary domain of two‐dimensional or three‐dimensional space. The existence of weak solutions of this problem is obtained.
D. A. Vorotnikov, V. G. Zvyagin
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The evolution of dust emitted by a uniform source above ground level
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 52, Page 3327-3343, 2003., 2003 A uniform source situated at a fixed location starts to emit dust at a certain time, t = 0, and maintains the same action for t > 0. The subsequent spread of the dust into space is governed by an initial boundary value problem of the atmospheric diffusion equation.
I. A. Eltayeb, M. H. A. Hassan
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