A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations

We study the well-posedness of the initial value problem for a wide class of singular evolution equations. We prove a general well-posedness theorem under three assumptions easy to check: the first controls the singular part of the equation, the second the behavior of the nonlinearities, and the third one assumes that an energy estimate can be found for the linearized system. We allow losses of derivatives in this energy estimate and therefore construct a solution by a Nash-Moser iterative scheme. As an application to this general theorem, we prove the well-posedness of the Serre and Green-Naghdi equation and discuss the problem of their validity as asymptotic models for the water-waves equations

Existence of travelling-wave solutions and local well-posedness of the Fowler equation

We study the existence of travelling-waves and local well-posedness in a subspace of $C_b^1(\mathbb{R})$ for a nonlinear evolution equation recently proposed by Andrew C. Fowler to study the dynamics of dunes.Comment: 21 page

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 by A. Constantin, D. Lannes "The hydrodynamical relevance of the Camassa-Holm and Degasperis-Processi equations" when the bottom is flat. We generalize here this result with a new class of equations taking into account variable bottom topographies. Of course, the many variable depth KdV equations existing in the literature are recovered as particular cases. Various regimes for the topography regimes are investigated and we prove consistency of these models, as well as a full justification for some of them. We also study the problem of wave breaking for our new variable depth and highly nonlinear generalizations of the KDV equations

Impacto de un Sistema Web para Optimizar Insumos en Negocio de Comida

Los avances tecnológicos han contribuido a que las empresas alcancen ventajas competitivas, tal como, la implementación de sistemas informáticos, los cuales aportan y cubren falencias de procesos de información. Si se habla de negocios de comida, uno de los principales objetivos es la gestión de los insumos y su inventario, con los cuales se busca reducir costos sin afectar la calidad de los productos. Por lo anteriormente expuesto, éste artículo tiene como objetivo analizar el impacto de una aplicación web desarrollada con metodología ágil Scrum, enfocándose en la optimización de los insumos de un local de comida. Para lograr esto, se consideraron tres etapas para la implementación: definición del producto, diseño de la solución y el desarrollo de la aplicación web; obteniendo como resultado, un sistema informático que permite mejorar el control de los inventarios; así como la planificación de adquisición y distribución de los insumos

Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations

We study the initial-value problem for a general class of nonlinear nonlocal coupled wave equations. The problem involves convolution operators with kernel functions whose Fourier transforms are nonnegative. Some well-known examples of nonlinear wave equations, such as coupled Boussinesq-type equations arising in elasticity and in quasi-continuum approximation of dense lattices, follow from the present model for suitable choices of the kernel functions. We establish local existence and sufficient conditions for finite time blow-up and as well as global existence of solutions of the problem.Comment: 11 pages. Minor changes and added reference

El urbanismo táctico y la participación ciudadana en el distrito de Comas 2021

Al pasar de los años se han presentado muchos problemas sociales en diversas partes del mundo, afectando las actividades del día a día. Esto es causado por los factores que se interponen entre la misma población, debido a la falta de desinterés hacia el espacioque lo rodea, sin tener en cuenta que la opinión del usuario es parte importante del lugar social; ya que, al dar importancia al espacio y al usuario en conjunto se va a generar un crecimiento social y cultural. El presente artículo pretende determinar, a través de una metodología de tipo aplicada, con nivel descriptiva-causal, enfoque mixto, diseño no experimental y método hipotético- deductivo, qué relación existe entre el urbanismo tacto y participación ciudadana. El urbanismo táctico es un instrumento provisional, que con apoyo del ciudadano se desarrolla comunitariamentegenerando cambios a su entorno, ese contiende estrategias para crear sociedad el cual requiere participación ciudadana de manera fundamental. La relación que ambas poseen es de importancia para el desarrollo positivo urbano

Simultaneous denoising and enhancement of signals by a fractal conservation law

In this paper, a new filtering method is presented for simultaneous noise reduction and enhancement of signals using a fractal scalar conservation law which is simply the forward heat equation modified by a fractional anti-diffusive term of lower order. This kind of equation has been first introduced by physicists to describe morphodynamics of sand dunes. To evaluate the performance of this new filter, we perform a number of numerical tests on various signals. Numerical simulations are based on finite difference schemes or Fast and Fourier Transform. We used two well-known measuring metrics in signal processing for the comparison. The results indicate that the proposed method outperforms the well-known Savitzky-Golay filter in signal denoising. Interesting multi-scale properties w.r.t. signal frequencies are exhibited allowing to control both denoising and contrast enhancement

Large time wellposdness to the 3-D Capillary-Gravity Waves in the long wave regime

In the regime of weakly transverse long waves, given long-wave initial data, we prove that the nondimensionalized water wave system in an infinite strip under influence of gravity and surface tension on the upper free interface has a unique solution on [0,{T}/\eps] for some \eps independent of constant $T.$ We shall prove in the subsequent paper \cite{MZZ2} that on the same time interval, these solutions can be accurately approximated by sums of solutions of two decoupled Kadomtsev-Petviashvili (KP) equations.Comment: Split the original paper(The long wave approximation to the 3-D capillary-gravity waves) into two parts, this is the first on