Results 11 to 20 of about 2,019,917 (274)

A Global Existence Theorem [PDF]

Canadian Mathematical Bulletin, 1966
The Cauchy-Peano existence theorem (1) does not allow us to decide from the form of a given system of equations whether or not its solution can be continued for the infinite interval -∞ < t < ∞. Several sufficient conditions for such a continuation were given by A. Wintner in (2). The main result of his paper is the following theorem which is not
Martin Eisen
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Co-Existence of Civilizations in the Global Era

Glocalism: Journal of Culture, Politics and Innovation, 2020
In the most general terms, “civilization” relates to the unique constitution of a “life-world”, defined by a coherent “worldview” (Weltanschauung) on the basis of continuity.
Hans Köchler
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Liapunov functions and global existence [PDF]

Bulletin of the American Mathematical Society, 1965
Aaron Strauss
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Global existence of solutions of differential inclusions

Journal of Mathematical Analysis and Applications, 1992
Assume that the Cauchy problem \(x'(t)\in F(t,x)\), \(x(t_ 0)=x_ 0\) has a local solution for every \(t_ 0\in[0,+\infty)\), \(x_ 0\in R^ n\). If \(v\) is a function such that \(v_ t+v_ xy\leq g(t,v(t,x))\) for every \(y\in F(t,x)\), \(v(t,x)\to\infty\) as \(| x|\to\infty\) and every maximal solution to \(u'=g(t,u)\) can be extended onto \([0,\infty)\),
Takeshi Taniguchi
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Global Existence for Nonlinear Diffusion Equations

Journal of Mathematical Analysis and Applications, 1995
The Dirichlet problem for degenerate reaction-diffusion-convection equations in space-dimension one is considered. Global existence of nonnegative solutions is studied. The role of convection in yielding global existence is analyzed in the special case when none of the three nonlinearities depends explicitly on \(x\) and \(t\).
Jeffrey R. Anderson, Kang Deng
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Existence of a Global Solution for a Viscoelastic System

Journal of Mathematical Analysis and Applications, 1998
The author considers the Cauchy problem for the viscoelastic system \[ v_t- u_x= 0,\quad u_t- f(v)_x+ ku= u_{xx} \] without the restriction that the initial data approach constants at infinity. Existence of unique classical solution is proved, including a priori estimates.
Yun‐guang Lu
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Global existence and stability of three species predator-prey system with prey-taxis

Mathematical Biosciences and Engineering, 2023
In this paper, we study the following initial-boundary value problem of a three species predator-prey system with prey-taxis which describes the indirect prey interactions through a shared predator, i.e., $ \begin{align*} \begin{cases} u_t = d ...
Gurusamy Arumugam
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Existence and smoothness of a class of Burgers equations

Partial Differential Equations in Applied Mathematics, 2021
In this paper we consider a class of Burgers equations. We propose a new method for investigation for existence of classical solutions.
Svetlin G. Georgiev, Gal Davidi
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On the global existence and blow-up for the double dispersion equation with exponential term

Electronic Research Archive, 2023
This paper deals with the initial boundary value problem for the double dispersion equation with nonlinear damped term and exponential growth nonlinearity in two space dimensions. We first establish the local well-posedness in the natural energy space by
Xiao Su, Hongwei Zhang
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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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