Results 61 to 70 of about 2,437,712 (232)

Boundedness and large time behavior of a signal-dependent motility system with nonlinear indirect signal production

Electronic Research Archive
In this paper, we study a chemotaxis system with nonlinear indirect signal production \begin{document}$ \left\{ {\begin{array}{*{20}{l}} {{u_t} = \Delta \left( {\gamma \left( v \right) u } \right)}+ru-\mu u^l, \quad &x\in \Omega, t>0, \\ {{v_t ...
Ya Tian, Jing Luo
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Global existence and decay rates of solutions for Vlasov–Navier–Stokes–Fokker–Planck equations with magnetic field

Mathematics Open, 2023
In this paper, we consider the two-phase flow model coupled by the incompressible magnetohydrodynamic equations and the discrete-phase (particle) dynamics equation Vlasov–Fokker–Planck in [Formula: see text].
Yingcong Song
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Existence of global solutions to the nonlocal Schrödinger equation on the line [PDF]

, 2023
Yi Zhao, Engui Fan
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Global Existence for the Confined Muskat Problem [PDF]

SIAM Journal on Mathematical Analysis, 2014
29 pages, 1 ...
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The critical case for a semilinear weakly hyperbolic equation

Electronic Journal of Differential Equations, 2004
We prove a global existence result for the Cauchy problem, in the three-dimensional space, associated with the equation $$ u_{tt}-a_lambda(t) Delta_x u=-u|u|^{p(lambda)-1} $$ where $a_lambda(t)ge 0$ and behaves as $(t-t_0)^lambda$ close to some $t_0 ...
Luca Fanelli, Sandra Lucente
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Sharp conditions of global existence for nonlinear Schrödinger equation with a harmonic potential

Advances in Nonlinear Analysis, 2019
The Cauchy problem of nonlinear Schrödinger equation with a harmonic potential for describing the attractive Bose-Einstein condensate under the magnetic trap is considered. We give some sufficient conditions of global existence and finite time blow up of
Zhang Mingyou, Ahmed Md Salik
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A note on the global existence and boundedness of an N-dimensional parabolic-elliptic predator-prey system with indirect pursuit-evasion interaction

Open Mathematics
We investigate the two-species chemotaxis predator-prey system given by the following system: ut=Δu−χ∇⋅(u∇w)+u(λ1−μ1ur1−1+av),x∈Ω,t>0,vt=Δv+ξ∇⋅(v∇z)+v(λ2−μ2vr2−1−bu),x∈Ω,t>0,0=Δw−w+v,x∈Ω,t>0,0=Δz−z+u,x∈Ω,t>0,\left\{\begin{array}{ll}{u}_{t}=\Delta u-\chi \
Liu Ling
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Liapunov fundtions and global existence without uniqueness [PDF]

Proceedings of the American Mathematical Society, 1970
In a recent paper J. Kato and A. Strauss character- ized the global existence of solutions of ani ordinary differenitial equation in terms of Liapunov functions in which they assumed the right hand side of the differential equatioln is locally Lipschitz. In the present paper a characterization of global existence of an ordinary differential equation is
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The Second Critical Exponent for a Time-Fractional Reaction-Diffusion Equation

Mathematics
In this paper, we consider the Cauchy problem of a time-fractional nonlinear diffusion equation. According to Kaplan’s first eigenvalue method, we first prove the blow-up of the solutions in finite time under some sufficient conditions.
Takefumi Igarashi
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Blow-up of radially symmetric solutions of a non-local problem modelling Ohmic heating

Electronic Journal of Differential Equations, 2002
We consider a non-local initial boundary-value problem for the equation $$ u_t=Delta u+lambda f(u)/Big(int_{Omega}f(u),dxBig)^2 ,quad x in Omega subset mathbb{R}^2 ,,;t>0, $$ where $u$ represents a temperature and $f$ is a positive and decreasing ...
Dimitrios E. Tzanetis
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