Results 11 to 20 of about 6,843,871 (313)
Optimal version of the Picard–Lindelöf theorem
Electronic Journal of Qualitative Theory of Differential Equations, 2021 Consider the differential equation $y'=F(x,y)$. We determine the weakest possible upper bound on $|F(x,y)-F(x,z)|$ which guarantees that this equation has for all initial values a unique solution, which exists globally.
Jan-Christoph Schlage-Puchta
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On a viscoelastic heat equation with logarithmic nonlinearity
Electronic Journal of Qualitative Theory of Differential Equations, 2022 This work deals with the following viscoelastic heat equations with logarithmic nonlinearity \begin{align*} u_t-\Delta u+\int_{0}^{t}g(t-s)\Delta u(s)ds=\vert u\vert^{p-2}u\ln\vert u\vert.
Nguyen Van Y, Nhan Le, Le Xuan Truong
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Global Existence of Near-Affine Solutions to the Compressible Euler Equations [PDF]
Archive for Rational Mechanics and Analysis, 2017 We establish the global existence of solutions to the compressible Euler equations, in the case that a finite volume of ideal gas expands into a vacuum.
S. Shkoller, T. Sideris
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The derivative NLS equation: global existence with solitons [PDF]
, 2017 We extend the global existence result for the derivative NLS equation to the case when the initial datum includes a finite number of solitons. This is achieved by an application of the B\"{a}cklund transformation that removes a finite number of zeros of ...
Yusuke Shimabukuro +2 more
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Global Existence for Capillary Water Waves [PDF]
Communications on Pure and Applied Mathematics, 2014 Consider the capillary water waves equations, set in the whole space with infinite depth, and consider small data (i.e., sufficiently close to zero velocity, and constant height of the water). We prove global existence and scattering. The proof combines in a novel way the energy method with a cascade of energy estimates, the space‐time resonance method
Germain, Pierre +2 more
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Global existence and boundedness for quasi-variational systems
International Journal of Mathematics and Mathematical Sciences, 1999 We consider quasi-variational ordinary differential systems, which may be considered as the motion law for holonomic mechanical systems. Even when the potential energy of the system is not bounded from below, by constructing appropriate Liapunov ...
Giancarlo Cantarelli
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Blow-up analysis for a doubly nonlinear parabolic system with multi-coupled nonlinearities
Electronic Journal of Qualitative Theory of Differential Equations, 2012 This paper deals with the global existence and the global nonexistence of a doubly nonlinear parabolic system coupled via both nonlinear reaction terms and nonlinear boundary flux.
Jian Wang, Yanyan Ge
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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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Existence and stability results of a nonlinear Timoshenko equation with damping and source terms [PDF]
Theoretical and Applied Mechanics, 2021 In this paper, we consider a nonlinear Timoshenko equation. First, we prove the local existence solution by the Faedo–Galerkin method, and, under suitable assumptions with positive initial energy, we prove that the local existence is global in time ...
Ouaoua Amar, Khaldi Aya, Maouni Messaoud
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Global existence and convergence rates to a chemotaxis-fluids system with mixed boundary conditions
Journal of Differential Equations, 2019 In this paper, we investigate the large time behavior of strong solutions to a chemotaxis-fluids system in an unbounded domain with mixed boundary conditions.
Yingping Peng, Zhaoyin Xiang
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