SASTRE GÓMEZ , Silvia

In this paper we consider the following nonlocal autonomous evolution equation in a bounded domain Ω in RN ∂tu(x,t)=−h(x)u(x,t)+g(∫ΩJ(x,y)u(y,t)dy)+f(x,u(x,t)) where h∈W1,∞(Ω), g:R→R and f:RN×R→R are continuously differentiable function, and J is a symmetric kernel; that is, J(x,y)=J(y,x) for any x,y∈RN. Under additional suitable assumptions on...

In this work we prove the equivalence between three different weak formulations of the steady periodic water wave problem where the vorticity is discontinuous. In particular, we prove that generalised versions of the standard Euler and stream function formulation of the governing equations are equivalent to a weak version of the recently...

The aim of this paper is to prove that a three dimensional Lagrangian flow which defines equatorially trapped water waves is dynamically possible. This is achieved by applying a mixture of analytical and topological methods to prove that the nonlinear exact solution to the geophysical governing equations, derived by Constantin (2012), is a...

We study a nonlocal version of the two-phase Stefan problem, which models a phase-transition problem between two distinct phases evolving to distinct heat equations. Mathematically speaking, this consists in deriving a theory for sign-changing solutions of the equation, u t = J ∗ v − v , v = Γ ( u ) , where the monotone graph is given by...

In this paper we present an analysis of the mean flow velocities, and related mass transport, which are induced by certain Equatorially-trapped water waves. In particular, we examine a recently-derived exact and explicit solution to the geophysical governing equations in the β−plane approximation at the Equator which incorporates a constant...

In this article we apply local bifurcation theory to prove the existence of small-amplitude steady periodic water waves, which propagate over a flat bed with a specified fixed mean-depth, and where the underlying flow has a discontinuous vorticity distribution.

The aim of this paper is to provide a comprehensive study of some linear non-local diffusion problems in metric measure spaces. These include, for example, open subsets in ℝN, graphs, manifolds, multi-structures and some fractal sets. For this, we study regularity, compactness, positivity and the spectrum of the stationary non-local operator....

In this paper we analyse the asymptotic behaviour of some nonlocal diffusion problems with local reaction term in general metric measure spaces. We find certain classes of nonlinear terms, including logistic type terms, for which solutions are globally defined with initial data in Lebesgue spaces. We prove solutions satisfy maximum and...

In this article, we study the existence of solutions of a parabolic-elliptic system of partial differential equations describing the behaviour of a biological species " " and a chemical stimulus " " in a bounded and regular domain of . The equation for is a parabolic equation with a nonlinear second order term of chemotaxis type with...

In this work we analyze the behavior of the solutions to nonlocal evolution equations of the form ut(x; t) = R J(x�����y)u(y; t) dy �����h"(x)u(x; t)+f(x; u(x; t)) with x in a perturbed domain " which is thought as a xed set from where we remove a subset A" called the holes. We choose an appropriated families of functions h" 2 L1 in...

The book contains a selection of contributions given at the 23th Congress on Differential Equations and Applications (CEDYA) / 13th Congress of Applied Mathematics (CMA) that took place at Castellon, Spain, in 2013. CEDYA is renowned as the congress of the Spanish Society of Applied Mathematics (SEMA) and constitutes the main forum and meeting...