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Global existence and global non-existence of solutions to a reaction-diffusion system
Nonlinear Analysis: Theory, Methods & Applications, 2000Let \(\Omega\) be a bounded domain in \(\mathbb{R}^n\) with \(C^2\) boundary \(\partial\Omega\). By a classification of the nonnegative real numbers, \(p_i\) and \(q_i\), \(i= 1,2\), several criteria for global existence and non-existence of positive solutions are given for the weakly coupled reaction-diffusion system \[ u_t= \Delta u+ u^{p_1} v^{q_1 ...
Sining Zheng
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On the Existence of a Global Solution of a Hyperbolic Problem
Doklady Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rozanova, O. S., Chizhonkov, E. V.
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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
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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
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ON GLOBAL EXISTENCE OF AN IMPLICIT FUNCTION
Russian Academy of Sciences. Sbornik Mathematics, 1994This article presents some new global implicit function theorems in the smooth case. The main idea of these results is based on special upper estimates for implicit functions that guarantees location of the graph of this function in a fixed domain. A row of theorems on that the graph of implicit functions is a smooth retract of Lebesgue neighborhoods ...
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Global Existence for the Relativistic Enskog Equations
Acta Mathematica Scientia, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huang, Jianjun, Jiang, Zhenglu
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On the Global Existence for the Kuramoto-Sivashinsky Equation
Journal of Dynamics and Differential Equations, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kukavica, Igor, Massatt, David
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Existence of Global Minima for Constrained Optimization
Journal of Optimization Theory and Applications, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ozdaglar, A. E., Tseng, P.
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2013
Abstract In Chapter 31, we prove future global existence in the case that the initial data are specified on the 3-torus, and assuming the initial data are close to those of de Sitter space. The proof is a bootstrap argument, one important ingredient being a system of differential inequalities.
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Abstract In Chapter 31, we prove future global existence in the case that the initial data are specified on the 3-torus, and assuming the initial data are close to those of de Sitter space. The proof is a bootstrap argument, one important ingredient being a system of differential inequalities.
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2003
Abstract This chapter contains a complete proof of the existence of global-in-time variational solutions for the full system of the Navier-Stokes equations of a viscous compressible and heat conducting fluid under suitable restrictions imposed on the constitutive laws.
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Abstract This chapter contains a complete proof of the existence of global-in-time variational solutions for the full system of the Navier-Stokes equations of a viscous compressible and heat conducting fluid under suitable restrictions imposed on the constitutive laws.
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