Uniform blow-up rates and asymptotic estimates of solutions for diffusion systems with nonlocal sources.
Uniform boundary stabilization of a thermoelastic bar with a nonlinear weak damping
Uniform energy decay rates of hyperbolic equations with nonlinear boundary and interior dissipation
Uniform exponential energy decay of Euler-Bernoulli equations by suitable boundary feedback operators
We study the uniform stabilization problem for the Euler-Bernoulli equation defined on a smooth bounded domain of any dimension with feedback dissipative operators in various boundary conditions.
Uniform stabilization for elastic waves system with highly nonlinear localized dissipation.
Uniform stabilization of solutions to a quasilinear wave equation with damping and source terms
In this note we prove the exponential decay of solutions of a quasilinear wave equation with linear damping and source terms.
Unique continuation and decay for the Korteweg-de Vries equation with localized damping
This work is devoted to prove the exponential decay for the energy of solutions of the Korteweg-de Vries equation in a bounded interval with a localized damping term. Following the method in Menzala (2002) which combines energy estimates, multipliers and compactness arguments the problem is reduced to prove the unique continuation of weak solutions. In Menzala (2002) the case where solutions vanish on a neighborhood of both extremes of the bounded interval where equation holds was solved combining...
Unique continuation and decay for the Korteweg-de Vries equation with localized damping
This work is devoted to prove the exponential decay for the energy of solutions of the Korteweg-de Vries equation in a bounded interval with a localized damping term. Following the method in Menzala (2002) which combines energy estimates, multipliers and compactness arguments the problem is reduced to prove the unique continuation of weak solutions. In Menzala (2002) the case where solutions vanish on a neighborhood of both extremes of the bounded interval where equation holds was solved combining...
Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations
Uniqueness and stability of regional blow-up in a porous-medium equation
Uniqueness of the boundary behavior for large solutions to a degenerate elliptic equation involving the ∞-Laplacian.
En esta nota estimamos la tasa máxima de crecimiento en la frontera de las soluciones de viscosidad de -Δ∞u + λ|u|m-1u = f en Ω (λ > 0, m > 3).De hecho, mostramos que sólo hay una única tasa de explosión en la frontera para esas soluciones explosivas. También obtenemos una versión del Teorema de Liouville para el caso Ω = RN.
Uniqueness of the critical mass blow up solution for the four dimensional gravitational Vlasov–Poisson system
Uniqueness of the Solution of a Semilinear Boundary Value Problem.
Universal solutions of a nonlinear heat equation on
In this paper, we study the relationship between the long time behavior of a solution of the nonlinear heat equation on (where ) and the asymptotic behavior as of its initial value . In particular, we show that if the sequence of dilations converges weakly to as , then the rescaled solution converges uniformly on to along the subsequence , where is an appropriate flow. Moreover, we show there exists an initial value such that the set of all possible attainable in this...
Unstable periodic wave solutions of nerve axion diffusion equations.
Upper estimate of the interval of existence of solutions of a nonlinear Timoshenko equation.
Upper Hausdorff dimension estimates for invariant sets of evolutionary systems on Hilbert manifolds
We prove a generalization of the Douady-Oesterlé theorem on the upper bound of the Hausdorff dimension of an invariant set of a smooth map on an infinite dimensional manifold. It is assumed that the linearization of this map is a noncompact linear operator. A similar estimate is given for the Hausdorff dimension of an invariant set of a dynamical system generated by a differential equation on a Hilbert manifold.
Upper semicontinuity of attractors of non-autonomous dynamical systems for small perturbations.
Upper semicontinuity of random attractors for non-compact random dynamical systems.
Variable depth KdV equations and generalizations to more nonlinear regimes
We study here the water waves problem for uneven bottoms in a highly nonlinear regime where the small amplitude assumption of the Korteweg-de Vries (KdV) equation is enforced. It is known that, for such regimes, a generalization of the KdV equation (somehow linked to the Camassa-Holm equation) can be derived and justified [Constantin and Lannes, Arch. Ration. Mech. Anal. 192 (2009) 165–186] when the bottom is flat. We generalize here this result with a new class of equations taking into account...