Percorrer por autor "Coelho, Maria Isabel Esteves"
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- Heteroclinic solutions of singular quasilinear bistable equationsPublication . Bonheure, Denis; Coelho, Maria Isabel Esteves; NYS, ManonIn this note we consider the action functional integral(R x ω) (1-root [1-(|∇u|)^2] + W(u) dx¯), where W is a double well potential and ω is a bounded domain of RN-1. We prove existence, one-dimensionality and uniqueness (up to translations) of a smooth minimizing phase transition between the two stable states u=-1 and u=1. The question of existence of at least one minimal heteroctinic connection for the non-autonomous model integral(R) (1-root [1-(|u’|)^2]+a(t)W(u))dt is also addressed. For this functional, we look for the possible assumptions on a(t) ensuring the existence of a minimizer.
- A one-dimensional prescribed curvature equation modeling the corneal shapePublication . Coelho, Maria Isabel Esteves; Corsato, Chiara; Omari, PierpaoloWe prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.
- A one-dimensional prescribed curvature equation modeling the corneal shape.Publication . Coelho, Maria Isabel Esteves; Corsato, Chiara; Omari, PierpaoloWe prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.
- Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ballPublication . Coelho, Maria Isabel Esteves; Corsato, Chiara; Rivetti, SabrinaWe study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.
- Travelling wave profiles in some models with nonlinear diffusionPublication . Coelho, Maria Isabel Esteves; Sanchez, LuisWe study some properties of the monotone solutions of the boundary value problem (p(u'))' - cu' + f(u) = 0, u(-infinity) = 0, u(+infinity) = 1, where f is a continuous function, positive in (0, 1) and taking the value zero at 0 and 1, and P may be an increasing homeomorphism of (0, 1) or (0, +infinity) onto [0, +infinity). This problem arises when we look for travelling waves for the reaction diffusion equation partial derivative u/partial derivative t = partial derivative/partial derivative x [p(partial derivative u/partial derivative x)] + f(u) with the parameter c representing the wave speed. A possible model for the nonlinear diffusion is the relativistic curvature operator p(nu)= nu/root 1-nu(2). The same ideas apply when P is given by the one- dimensional p- Laplacian P(v) = |v|(p-2)v. In this case, an advection term is also considered. We show that, as for the classical Fisher- Kolmogorov- Petrovski- Piskounov equations, there is an interval of admissible speeds c and we give characterisations of the critical speed c. We also present some examples of exact solutions. (C) 2014 Elsevier Inc. All rights reserved.