Global existence and nonlinear boundary stabilization of an elastic system. (Existence globale et stabilisation frontière non linéaire d'un système d'élasticité.)
Global existence and polynomial decay for a problem with Balakrishnan-Taylor damping
A viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping is considered. Using integral inequalities and multiplier techniques we establish polynomial decay estimates for the energy of the problem. The results obtained in this paper extend previous results by Tatar and Zaraï [25].
Global existence and stability of solution for a nonlinear Kirchhoff type reaction-diffusion equation with variable exponents
We consider a class of Kirchhoff type reaction-diffusion equations with variable exponents and source terms We prove with suitable assumptions on the variable exponents the global existence...
Global existence for a quasilinear wave equation outside of star-shaped domains
This talk describes joint work with Chris Sogge and Markus Keel, in which we establish a global existence theorem for null-type quasilinear wave equations in three space dimensions, where we impose Dirichlet conditions on a smooth, compact star-shaped obstacle . The key tool, following Christodoulou [1], is to use the Penrose compactification of Minkowski space. In the case under consideration, this reduces matters to a local existence theorem for a singular obstacle problem. Full details will...
Global existence for coupled Klein-Gordon equations with different speeds
Consider, in dimension 3, a system of coupled Klein-Gordon equations with different speeds, and an arbitrary quadratic nonlinearity. We show, for data which are small, smooth, and localized, that a global solution exists, and that it scatters. The proof relies on the space-time resonance approach; it turns out that the resonant structure of this equation has features which were not studied before, but which are generic in some sense.
Global existence for nonlinear system of wave equations in 3-D domains
We study the initial-boundary problem for a nonlinear system of wave equations with Hamilton structure under Dirichlet's condition. We use the local-in-time Strichartz estimates from [Burq et al., J. Amer. Math. Soc. 21 (2008), 831-845], Morawetz-Pohožaev's identity derived in [Miao and Zhu, Nonlinear Anal. 67 (2007), 3136-3151], and an a priori estimate of the solutions restricted to the boundary to show the existence of global and unique solutions.
Global existence for quasi-linear dissipative hyperbolic equations with large data and small parameter
Global Existence for Quasi-Linear Dissipative Wave Equations with Large Data and Small Parameter.
Global existence for the nonlinear equations of crystal optics
Global existence of low regularity solutions of non-linear wave equations.
Global existence of small radially symmetric solutions to quadratic nonlinear evolution equations in an exterior domain.
Global existence of small radially symmetric solutions to quadratic nonlinear wave equations in an exterior domain.
Global existence of solutions for the 1-D radiative and reactive viscous gas dynamics
In this paper, we prove the existence of a global solution to an initial-boundary value problem for 1-D flows of the viscous heat-conducting radiative and reactive gases. The key point here is that the growth exponent of heat conductivity is allowed to be any nonnegative constant; in particular, constant heat conductivity is allowed.
Global existence of strong solutions to the one-dimensional full model for phase transitions in thermoviscoelastic materials
This paper is devoted to the analysis of a one-dimensional model for phase transition phenomena in thermoviscoelastic materials. The corresponding parabolic-hyperbolic PDE system features a strongly nonlinear internal energy balance equation, governing the evolution of the absolute temperature , an evolution equation for the phase change parameter , including constraints on the phase variable, and a hyperbolic stress-strain relation for the displacement variable . The main novelty of the model...
Global existence, uniqueness, and asymptotic behavior of solution for -Laplacian type wave equation.
Global in time solutions to quasilinear telegraph equations involving operators with time delay
The existence of small global (in time) solutions to an abstract evolution equation containing a damping term is proved. The result is then applied to fully nonlinear telegraph equations and to nonlinear equations involving operators with time delay.
Global in time solvability of the initial boundary value problem for some nonlinear dissipative evolution equations
The global in time solvability of the one-dimensional nonlinear equations of thermoelasticity, equations of viscoelasticity and nonlinear wave equations in several space dimensions with some boundary dissipation is discussed. The blow up of the solutions which might be possible even for small data is excluded by allowing for a certain dissipative mechanism.
Global in Time Stability of Steady Shocks in Nozzles
We prove global dynamical stability of steady transonic shock solutions in divergent quasi-one-dimensional nozzles. One of the key improvements compared with previous results is that we assume neither the smallness of the slope of the nozzle nor the weakness of the shock strength. A key ingredient of the proof are the derivation a exponentially decaying energy estimates for a linearized problem.
Global infinite energy solutions of the critical semilinear wave equation.
Global Instability and Essential Spectrum in Semilinear Evolution Equations.