1,721,193 research outputs found
Well-posedness of a system of transport and diffusion equations in space of measures
No full textIn this paper, we establish the well-posedness of the following system of two transport equations coupled with a diffusion equation: ∂tμt1+∇⋅(v1[μt]μt1)=N1(t,μt),∂tμt2−Δμt2=N2(t,μt),∂tμt3+∇⋅(v2[μt]μt3)=N3(t,μt), in Rd where μt1,μt2,μt3 are finite signed measures. Here, the vector field v1, v2 and the source term N1,N2,N3 depend on the measure-valued solution vector μt=(μt1,μt2,μt3).Fil: Ackleh, Azmy S.. State University of Louisiana; Estados UnidosFil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
Diffusive limit to a selection-mutation equation with small mutation formulated on the space of measures
No full textIn this paper we consider a selection-mutation model with an advection term formulated on the space of finite signed measures on Rd. The selection-mutation kernel is described by a family of measures which allows the study of continuous and discrete kernels under the same setting. We rescale the selection-mutation kernel to obtain a diffusively rescaled selection-mutation model. We prove that if the rescaled selection-mutation kernel converges to a pure selection kernel then the solution of the diffusively rescaled model converges to a solution of an advection-diffusion equation.Fil: Ackleh, Azmy S.. State University of Louisiana; Estados UnidosFil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
Weighted embedding theorems for radial Besov and Triebel-Lizorkin spaces
Full text linkWe study the continuity and compactness of embeddings for radial Besov and Triebel-Lizorkin spaces with weights in the Muckenhoupt class A∞. The main tool is a discretization in terms of an almost orthogonal wavelet expansion adapted to the radial situation.Fil: de Napoli, Pablo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaFil: Drelichman, Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaFil: Saintier, Nicolas Bernard Claude. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentin
Finite difference schemes for a structured population model in the space of measures
Full text linkWe present two finite-difference methods for approximating solutions to a structured population model in the space of non-negative Radon Measures. The first method is a first-order upwind-based scheme and the second is high-resolution method of second-order. We prove that the two schemes converge to the solution in the Bounded-Lipschitz norm. Several numerical examples demonstrating the order of convergence and behavior of the schemes around singularities are provided. In particular, these numerical results show that for smooth solutions the upwind and high-resolution methods provide a first-order and a second-order approximation, respectively. Furthermore, for singular solutions the second-order high-resolution method is superior to the first-order method.Fil: Ackleh, Azmy S.. State University of Louisiana; Estados UnidosFil: Lyons, Rainey. State University of Louisiana; Estados UnidosFil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
Opinion fitness and convergence to consensus in homogeneous and heterogeneous populations
No full textIn this work we study the formation of consensus in homogeneous and heterogeneous populations, and the effect of attractiveness or fitness of the opinions. We derive the corresponding kinetic equations, analyze the long time behavior of their solutions, and characterize the consensus opinion.Fil: Pérez Llanos, Mayte. Universidad de Sevilla; EspañaFil: Pinasco, Juan Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas 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: Saintier, Nicolas Bernard Claude. Consejo Nacional de Investigaciones Científicas 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"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentin
Sensitivity equations for measure-valued solutions to transport equations
Full text linkWe consider the following transport equation in the space of bounded, nonnegative Radon measures M+(Rd): θtμt + θx(v(x)μt) = 0: We study the sensitivity of the solution μt with respect to a perturbation in the vector field, v(x). In particular, we replace the vector field v with a perturbation of the form vh = v0(x) + hv1(x) and let μh t be the solution of θtμh t + θx(vh(x)μh t) = 0: We derive a partial differential equation that is satisfied by the derivative of μh t with respect to h, θh(μh t). We show that this equation has a unique very weak solution on the space Z, being the closure of M(Rd) endowed with the dual norm (C1,α(Rd))*. We also extend the result to the nonlinear case where the vector field depends on μt, i.e., v = v[μt](x).Fil: Ackleh, Azmy S.. State University of Louisiana; Estados UnidosFil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Skrzeczkowski, Jakub. University of Warsaw; Poloni
Non-local Equations and Optimal Sobolev Inequalities on Compact Manifolds
No full textThis paper deals with the theory of fractional Sobolev spaces on a compact Riemannian manifold (M, g). Our first main result shows that the fractional Sobolev spaces Ws,p(M) introduced by Guo et al. (Electron J Differ Equ 2018(156): 1–17, 2018) coincide with the classical Triebel–Lizorkin spaces (which in turn coincide with the Besov spaces). As an application, we study a non-local elliptic equation of the form LKu + h|u| p−2u = f |u| q−2u, (1) where the operator LK u is an integro-differential operator a little more general than the fractional Laplacian, defined on Ws,p(M). We use the Mountain Pass Theorem to show an existence result under a coercivity condition when we have a sub-critical non-linearity on the right-hand side of the Eq. (1). Our second main result is a Sobolev inequality in the critical range with an optimal constant for the fractional Sobolev spaces Ws,2(M). This inequality gives us a sufficient existence condition for (1) with p = 2 and q = 2∗ = 2n n−2s the fractional critical Sobolev exponent.Fil: Rey, Carolina Ana. Universidad Tecnica Federico Santa Maria.; Chile. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentin
A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces
Full text linkIn this paper, we study the critical Sobolev embeddings W1,p(.)(Ω)⊂Lp*(.)(Ω) for variable exponent Sobolev spaces from the point of view of the Γ-convergence. More precisely we determine the Γ-limit of subcritical approximation of the best constant associated with this embedding. As an application we provide a sufficient condition for the existence of extremals for the best constant.Fil: Fernandez Bonder, Julian. Consejo Nacional de Investigaciones Científicas 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"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Saintier, Nicolas Bernard Claude. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Silva, Analia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentin
Kinetic theory of active particles meets auction theory
No full textIn this paper we study Nash equilibria in auctions from the kinetic theory of activeparticles point of view. We propose a simple learning rule for agents to update theirbidding strategies based on their previous successes and failures, in first-price auctionswith two bidders. Then, we formally derive the corresponding kinetic equations whichdescribe the evolution over time of the distribution of agents on the bidding strategies.We show that the stationary solution of the equation corresponds to the symmetric Nashequilibrium of the auction, and we prove the convergence to this stationary solutionwhen time goes to infinity. We also introduce a more general learning rule that onlydepends on the income of agents, and we apply to both first- and second-price auctions.We show that agents learn the Nash equilibrium in first- and second-price auctions with these rules. We present agent-based simulations of the models, and we discuss severalopen problems.Fil: Crucianelli, Carla. University of Princeton; Estados UnidosFil: Pinasco, Juan Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas 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: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentin
The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis–Nirenberg problem
Full text linkIn this paper we extend the well-known concentration-compactness principle for the Fractional Laplacian operator in unbounded domains. As an application we show sufficient conditions for the existence of solutions to some critical equations involving the fractional p-Laplacian in the whole Rn.Fil: Bonder, Julián Fernández. Consejo Nacional de Investigaciones Científicas 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"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Silva, Analía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentin
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