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We study the stabilization of global solutions of the
Kawahara (K) equation in a bounded interval, under the effect of
a localized damping mechanism. The Kawahara equation is a model
for small amplitude long waves. Using multiplier techniques and
compactness arguments we prove the
exponential decay of the solutions of the (K) model. The proof
requires of a unique continuation theorem and the smoothing effect
of the (K) equation on the real line, which are proved in this work.
In this paper we study a one dimensional model of ferromagnetic nano-wires of finite length. First we justify the model by Γ-convergence arguments. Furthermore we prove the existence of wall profiles. These walls being unstable, we stabilize them by the mean of an applied magnetic field.
In this paper we study a one dimensional model of ferromagnetic nano-wires of finite
length. First we justify the model by Γ-convergence arguments.
Furthermore we prove the existence of wall profiles. These walls being unstable, we
stabilize them by the mean of an applied magnetic field.
In this paper we study a one dimensional model of ferromagnetic nano-wires of finite
length. First we justify the model by Γ-convergence arguments.
Furthermore we prove the existence of wall profiles. These walls being unstable, we
stabilize them by the mean of an applied magnetic field.
This note summarizes the results obtained in [30]. We exhibit stable finite time blow up regimes for the energy critical co-rotational Wave Map with the target in all homotopy classes and for the equivariant critical Yang-Mills problem. We derive sharp asymptotics on the dynamics at blow up time and prove quantization of the energy focused at the singularity.
The isothermal Navier–Stokes–Korteweg system is used to model dynamics of a compressible fluid exhibiting phase transitions between a liquid and a vapor phase in the presence of capillarity effects close to phase boundaries. Standard numerical discretizations are known to violate discrete versions of inherent energy inequalities, thus leading to spurious dynamics of computed solutions close to static equilibria (e.g., parasitic currents). In this work, we propose a time-implicit discretization of...
The paper considers the static Maxwell system for a Lipschitz domain with perfectly conducting boundary. Electric and magnetic permeability ε and μ are allowed to be monotone and Lipschitz continuous functions of the electromagnetic field. The existence theory is developed in the framework of the theory of monotone operators.
Nonlinear Schrödinger equations are usually investigated with the use of the variational methods that are limited to energy-subcritical dimensions. Here we present the approach based on the shooting method that can give the proof of existence of the ground states in critical and supercritical cases. We formulate the assumptions on the system that are sufficient for this method to work. As examples, we consider Schrödinger-Newton and Gross-Pitaevskii equations with harmonic potentials.
The existence of steady states in the microcanonical case for a system describing the interaction of gravitationally attracting particles with a self-similar pressure term is proved. The system generalizes the Smoluchowski-Poisson equation. The presented theory covers the case of the model with diffusion that obeys the Fermi-Dirac statistic.
We investigate stationary energy models in heterostructures consisting of continuity equations for all involved species, of a Poisson equation for the electrostatic potential and of an energy balance equation. The resulting strongly coupled system of elliptic differential equations has to be supplemented by mixed boundary conditions. If the boundary data are compatible with thermodynamic equilibrium then there exists a unique steady state. We prove that in a suitable neighbourhood of such a thermodynamic...
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