186 research outputs found
Existence, uniqueness and decay rates for evolution equations on trees
We study evolution equations governed by an averaging operator on a directed tree, showing existence and uniqueness of solutions. In addition we find conditions of the initial condition that allows us to find the asymptotic decay rate of the solutions as . It turns out that this decay rate is not uniform, it strongly depends on how the initial condition goes to zero as one goes down in the tree.Fil: del Pezzo, Leandro Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Mosquera, Carolina Alejandra. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Rossi, Julio Daniel. Universidad de Alicante; España. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentin
The unique continuation property for a nonlinear equation on trees
In this paper, we study the game p-Laplacian on a tree, that is, u(x) = α / 2 max y∈S(x) u(y) + min y∈S(x) u(y) + β m y∈S(x) u(y);here x is a vertex of the tree and S(x) is the set of successors of x. We study the family of the subsets of the tree that enjoy the unique continuation property, that is, subsets U such that u |U = 0 implies u ≡ 0.Fil: del Pezzo, Leandro Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Mosquera, Carolina Alejandra. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Rossi, Julio Daniel. Universidad de Alicante; España. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentin
Tug-of-War games and the infinity Laplacian with spatial dependence
In this paper we look for PDEs that arise as limits of values
of Tug-of-War games when the possible movements of the game are
taken in a family of sets that are not necessarily euclidean balls. In this
way we ¯nd existence of viscosity solutions to the Dirichlet problem for
an equation of the form ¡hD
2
v ¢ Jx(Dv); Jx(Dv)i(x) = 0, that is, an
in¯nity Laplacian with spatial dependence. Here Jx(Dv(x)) is a vector
that depends on the the spatial location and the gradient of the solution.Fil: Gomez, Ivana Daniela. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico - CONICET - Santa Fe. Instituto de Matemática Aplicada; Argentina;Fil: Rossi, Julio Daniel. Universidad de Buenos Aires; Argentina
Explosion time in stochastic differential equations with small diffusion
We consider solutions of a one dimensional stochastic differential equations that explode in finite time. We prove that, under suitable hypotheses, the explosion time converges almost surely to the one of the ODE governed by the drift term when the diffusion coefficient approaches zero.Fil: Groisman, Pablo Jose. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Rossi, Julio Daniel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentin
Complete Blow-up and Avalanche Formation for a Parabolic System with Non-Simultaneous Blow-up
We study the possibility of defining a nontrivial continuation after the blow-up time for a system of two heat equations with a nonlinear coupling at the boundary. It turns out that any possible continuation that verify a maximum principle is identically infinity after the blow-up time, that is, both components blow up completely. We also analyze the propagation of the singularity to the whole space, the avalanche, when blow-up is non-simultaneous.Fil: Brändle, Cristina. Universidad Carlos III de Madrid. Departamento de Matemáticas; ArgentinaFil: Quirós, Fernando. Universidad Autónoma de Madrid; EspañaFil: Rossi, Julio Daniel. Universidad Autónoma de Madrid; España. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentin
A complete classification of simultaneous blow-up rates
We study the simultaneous blow-up rates of a system of two heat equations coupled through the boundary in a nonlinear way. We complete the previous known results by covering the whole range of possible parameters.Fil: Brändle, Cristina. Universidad Autónoma de Madrid; EspañaFil: Quirós, Fernando. Universidad Autónoma de Madrid; EspañaFil: Rossi, Julio Daniel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentin
Local and nonlocal energy-based coupling models
In this paper we study two different ways of coupling a local operator with a nonlocal one so that the resulting equation is related to an energy functional. In the first strategy the coupling is given via source terms in the equation, and in the second one a flux condition in the local part appears. For both models we prove existence and uniqueness of a solution that is obtained via direct minimization of the related energy functional. In the second part of this paper we extend these ideas to local/nonlocal elasticity models in which we couple classical local elasticity with nonlocal peridynamics.Fil: Acosta, Gabriel. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Bersetche, Francisco. Universidad Tecnica Federico Santa Maria.; ChileFil: Rossi, Julio Daniel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentin
Nontrivial compact blow-up sets of lower dimension in a half-space
No posee DOIIn this paper we provide examples of blowing-up solutions to parabolic problems in a half space, RN+×RM={xN>0}×RMR+N×RM={xN>0}×RM, with nontrivial blow-up sets of dimension strictly smaller than the space dimension. To this end we prove existence of a nontrivial compactly supported solution to ∇(|∇φ|p−2∇φ)=φ∇(|∇φ|p−2∇φ)=φ in the half space RN+={xN>0}R+N={xN>0} with the nonlinear boundary condition −|∇φ|p−2∂φ∂xN=φp−1−|∇φ|p−2∂φ∂xN=φp−1 on ∂RN+={xN=0}∂R+N={xN=0}
Conjuntos de explosión de dimensión menor en el semiespacio
Nuestro principal objetivo en este trabajo es encontrar algunos ejemplos de soluciones de problemas parabólicos en el semiespacio, R N + × RM = {xN > 0} × RM que explotan, cuyos conjuntos de explosión son no triviales y de dimensión estrictamente menor que la dimensión del espacio ambiente. Con este fin probamos la existencia de soluciones no triviales de soporte compacto de ∇(|∇ϕ| p−2∇ϕ) = ϕ m en el semiespacio R N + con la condición de borde no lineal −|∇ϕ| p−2 ∂ϕ ∂xN = ϕ p−1 sobre ∂R N + = {xN = 0}
The best Sobolev trace constant in periodic media for critical and subcritical exponents
In this paper we study homogenisation problems for Sobolev trace embedding H1(Ω) ↪ Lq(∂Ω) in a bounded smooth domain. When q = 2 this leads to a Steklov-like eigenvalue problem. We deal with the best constant of the Sobolev trace embedding in rapidly oscillating periodic media, and we consider H1 and Lq spaces with weights that are periodic in space. We find that extremals for these embeddings converge to a solution of a homogenised limit problem, and the best trace constant converges to a homogenised best trace constant. Our results are in fact more general; we can also consider general operators of the form aÉ›(x, ∇u) with non-linear Neumann boundary conditions. In particular, we can deal with the embedding W1,p(Ω) ↪ Lq(∂Ω).Fil: Fernandez Bonder, Julian. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Orive, Rafael. Universidad Autónoma de Madrid; EspañaFil: Rossi, Julio Daniel. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentin
- …