On the global existence and blowup of smooth solutions to the multi-dimensional compressible Euler equations with time-depending damping [PDF]
, 2016 In this paper, we are concerned with the global existence and blowup of smooth solutions to the multi-dimensional compressible Euler equations with time-depending damping {∂tρ+div (ρu)=0,∂t(ρu)+div (ρu⊗u+pId)=−α(t)ρu,ρ(0,x)=ρ¯+ερ0(x),u(0,x)=εu0(x), where
Fei Hou, Huicheng Yin
semanticscholar +1 more source
Uniform boundedness and extinction results of solutions to a predator–prey system
Electronic Journal of Qualitative Theory of Differential Equations, 2020 Global existence, positivity, uniform boundedness and extinction results of solutions to a system of reaction-diffusion equations on unbounded domain modeling two species on a predator–prey relationship is considered.
Mokhtar Kirane +2 more
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Global existence and finite time blow-up of solutions to a nonlocal p-Laplace equation
Mathematical Modelling and Analysis, 2019 In this paper a class of nonlocal diffusion equations associated with a p-Laplace operator, usually referred to as p-Kirchhoff equations, are studied.
Jian Li, Yuzhu Han
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Global solvability of a chemotaxis-haptotaxis model in the whole 2-d space
Mathematical Biosciences and Engineering, 2023 This paper investigates a two-dimensional chemotaxis-haptotaxis model $ \begin{eqnarray*} \left\{\begin{array}{lll} u_t = \Delta u-\chi\nabla\cdot(u\nabla v)-\xi\nabla\cdot(u\nabla w),&{} x\in\mathbb{R}^2,\ t>0,\\ v_t = \Delta v-v+u ...
Meng Liu, Yuxiang Li
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Global existence of small-norm solutions in the reduced Ostrovsky equation [PDF]
, 2013 We use a novel transformation of the reduced Ostrovsky equation to the integrable Tzitz\'eica equation and prove global existence of small-norm solutions in Sobolev space $H^3(R)$.
Grimshaw, Roger, Pelinovsky, Dmitry
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On a price formation free boundary model by Lasry & Lions: The Neumann problem [PDF]
, 2011 We discuss local and global existence and uniqueness for the price formation free boundary model with homogeneous Neumann boundary conditions introduced by Lasry & Lions in 2007.
Caffarelli, Luis A. +2 more
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Asymptotic behavior of solutions for linear evolutionary boundary value problem of viscoelastic damped wave equation [PDF]
Mathematica Bohemica, 2020 We study the existence of global in time and uniform decay of weak solutions to the initial-boundary value problem related to the dynamic behavior of evolution equation accounting for rotational inertial forces along with a linear nonlocal frictional ...
Mohamed Berbiche
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A sufficient condition for global existence of solutions to a generalized derivative nonlinear Schrödinger equation [PDF]
, 2016 We give a sufficient condition for global existence of the solutions to a generalized derivative nonlinear Schr\"{o}dinger equation (gDNLS) by a variational argument.
Noriyoshi Fukaya +2 more
semanticscholar +1 more source
Global existence for a nonlocal model for adhesive contact
, 2017 In this paper we address the analytical investigation of a model for adhesive contact, which includes nonlocal sources of damage on the contact surface, such as the elongation.
Bonetti, Elena +2 more
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Coercivity and stability results for an extended Navier-Stokes system
, 2012 In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role of divergence
Abels H. +11 more
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