L. F. Chacón-Cortés

• Doctor of Philosophy
• Professor (Assistant) at Pontifical Xavierian University

We introduce discrete and p-adic continuous versions of the Schnakenberg system on a one-dimensional p-adic unit ball. We establish criteria for the existence of Turing patterns in p-adic Schnakenberg systems. We give extensive simulations of some of these systems. We present numerical simulations that illustrate the shape of the Turing patterns in...

We introduce discrete and p-adic continuous versions of the FitzHugh-Nagumo system on the one-dimensional p-adic unit ball. We provide criteria for the existence of Turing patterns. We present extensive simulations of some of these systems. The simulations show that the Turing patterns are traveling waves in the p-adic unit ball.

We introduce a new family of p-adic non-linear evolution equations. We establish the local well-posedness of the Cauchy problem for these equations in Sobolev-type spaces. For a certain subfamily, we show that the blow-up phenomenon occurs and provide numerical simulations showing this phenomenon.

In this paper, we prove the boundedness of the fractional maximal and the fractional integral operator in the -adic variable exponent Lebesgue spaces. As an application, we show the existence and uniqueness of the solution for a nonhomogeneous Cauchy problem in the -adic variable exponent Lebesgue spaces. 1. Introduction The field of -adic numbers...

We study the well-posed problem for general p-adic nonlocal semilinear ultradiffusion equations and the emergence of finite time blow-up for their solutions. In particular, we prove that this phenomenon does appear under appropriate assumptions on the nonlinear term. Finally, we illustrate and study by numerical means the behavior of blow-up for a...

This work is dedicated to study the pseudodifferential operator \((D^\alpha _{d_1,d_2} \varphi )(x)=-\int \limits _{{\mathbb {Q}}_p^n} {\mathcal {A}}^{-\alpha }_{d_1,d_2}(y) [\varphi (x+y)-\varphi (x)] d^ny\), which can be seen as a generalization of Taibleson operator; here \({\mathcal {A}}^{\alpha }_{d_1,d_2}(x)=\max \left\{ \left\| x\right\| _p^...

In this paper we introduce variable exponent Lebesgue spaces where the underlying space is the field of the p-adic numbers. We prove many properties of the spaces and also study the boundedness of the maximal operator as well as its application to convolution operators.

The main goal of this article is to study a new class of nonlocal operators and the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated with them. The fundamental solutions of these equations are transition functions of Markov processes on an n-dimensional vector space over the p-adic numbers. We also study s...

The problem of existence of solutions to p-adic semilinear heat equations with particular nonlinear terms has already been studied in the literature but the occurrence of blow-up phenomena has not been considered yet. We initiate the study of finite time blow-up for solutions of this kind of p-adic semilinear equations, proving that this phenomenon...

In this article we initiate the study of the heat traces and spectral zeta functions for certain p-adic Laplacians. We show that the heat traces are given by p-adic integrals of Laplace type, and that the spectral zeta functions are p-adic integrals of Igusa-type. We find good estimates for the behaviour of the heat traces when the time tends to in...

En este artculo se estudia el problema del primer retorno asociado a ciertos operadores pseudo-diferenciales elípticos en dimensiones 4 y 2 sobre los números p-ádicos. Este tipo de problemas esta conectado con ciertos modelos de sistemas complejos

In this article we initiate the study of the heat traces and spectral zeta functions for certain p-adic Laplacians. We show that the heat traces are given by p-adic integrals of Laplace type, and that the spectral zeta functions are p-adic integrals of Igusa-type. We find good estimates for the behaviour of the heat traces when the time tends to in...

In this article we study the problem of the first passage time associated to certain elliptic pseudodifferential operators in dimensions 4 and 2 over the p-adics. This type of problems appeared in connection with certain models of complex systems.

In this article, we introduce a new class of parabolic-type pseudo differential equations with variable coefficients over the p-adics. We establish the existence and uniqueness of solutions for the Cauchy problem associated with these equations. The fundamental solutions of these equations are connected with Markov processes. Some of these equation...

In this article we introduce a new type of nonlocal operators and study the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated to these operators. Some of these equations are the p-adic master equations of certain models of complex systems introduced by Avetisov et al. The fundamental solutions of these para...