Results 51 to 60 of about 309 (70)
Global and exponential attractors for the Penrose-Fife system [PDF]
arXiv, 2008 The Penrose-Fife system for phase transitions is addressed. Dirichlet boundary conditions for the temperature are assumed. Existence of global and exponential attractors is proved. Differently from preceding contributions, here the energy balance equation is both singular at 0 and degenerate at infinity.
arxiv
Non-linear partial differential equations with discrete state-dependent delays in a metric space [PDF]
arXiv, 2009 We investigate a class of non-linear partial differential equations with discrete state-dependent delays. The existence and uniqueness of strong solutions for initial functions from a Banach space are proved. To get the well-posed initial value problem we restrict our study to a smaller metric space, construct the dynamical system and prove the ...
arxiv
A nonlinear transmission problem for a compound plate with thermoelastic part [PDF]
arXiv, 2010 In this paper we study a nonlinear transmission problem for a plate which consists of thermoelastic and isothermal parts. The problem generates a dynamical system in a suitable Hilbert space. Main result is the proof of the asymptotic smoothness of this dynamical system. Also we prove the existence of a compact global attractor in particular cases when
arxiv
Non-local PDEs with a state-dependent delay term presented by Stieltjes integral [PDF]
arXiv, 2010 Parabolic partial differential equations with state-dependent delays (SDDs) are investigated. The delay term presented by Stieltjes integral simultaneously includes discrete and distributed SDDs. The singular Lebesgue-Stieltjes measure is also admissible. The conditions for the corresponding initial value problem to be well-posed are presented.
arxiv
Long-time dynamics of the parabolic $p$-Laplacian equation [PDF]
arXiv, 2012 In this paper, we study the long-time behaviour of solutions of Cauchy problem for the parabolic $p$-Laplacian equation with variable coefficients. Under mild conditions on the coefficient of the principal part and without upper growth restriction on the source function, we prove that this problem possesses a compact and invariant global attractor in ...
arxiv
Strongly damped wave equation with exponential nonlinearities [PDF]
arXiv, 2012 In this paper, we study the initial boundary value problem for the two dimensional strong damped wave equation with exponentially growing source and damping terms. We first show the well-posedness of this problem and then prove the existence of the global attractor in $(H_{0}^{1}(\Omega)\cap L^{\infty}(\Omega))\times L^{2}(\Omega)$.
arxiv
Periodic and Almost Periodic Random Inertial Manifolds for Non-Autonomous Stochastic Equations [PDF]
arXiv, 2014 By the Lyapunov-Perron method,we prove the existence of random inertial manifolds for a class of equations driven simultaneously by non-autonomous deterministic and stochastic forcing. These invariant manifolds contain tempered pullback random attractors if such attractors exist.
arxiv
Convergences of asymptotically autonomous pullback attractors towards semigroup attractors [PDF]
arXiv, 2017 For pullback attractors of asymptotically autonomous dynamical systems we study the convergences of their components towards the global attractors of the limiting semigroups. We use some conditions of uniform boundedness of pullback attractors, instead of uniform compactness conditions used in the literature.
arxiv
Invariant measures for systems of Kolmogorov equations [PDF]
arXiv, 2017 In this paper we provide sufficient conditions which guarantee the existence of a system of invariant measures for semigroups associated to systems of parabolic differential equations with unbounded coefficients. We prove that these measures are absolutely continuous with respect to the Lebesgue measure and study some of their main properties. Finally,
arxiv
Global attractor for a nonlinear one-dimensional compressible viscous micropolar fluid [PDF]
arXiv, 2018 This paper considers the dynamical behavior of solutions of constitutive systems for 1D compressible viscous and heat-conducting micropolar fluids. With proper constraints on initial data, we prove the existence of global attractors in generalized Sobolev spaces $H^{(1)}_{\delta}$ and $H^{(2)}_{\delta}$.
arxiv