7 citations · 12 across the 10 of their papers we have counts for
11 papers
Some stochastic process techniques applied to deterministic models
Eric José Ávila-Vales, José Villa-Morales
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical…
An Application of Fractional Calculus to Column Theory
José Villa-Morales, Manuel Ramírez-Aranda
In this article, we employ a fractional version of the radius of curvature in Euler's equation for column buckling, enabling us to derive a fractional differential equation in the…
Upper bounds for the blow-up time of a system of fractional differential equations with Caputo derivatives and a numerical scheme for the solution of the system
José Villa-Morales
The article provides upper bounds for the blow-up time of a system of fractional differential equations in the Caputo sense. Furthermore, concrete examples of blow-up time estimati…
The set of -harmonic functions in is total in
José Villa-Morales
Let , with , be the fractional -Laplacian operator. We prove that the span of -harmonic functions in is dense in .
Blow-up at space infinity for solutions of a system of non-autonomous semilinear heat equations
Gabriela de Jesús Cabral-García, José Villa-Morales
In this paper we will see that the global or local existence of solutions to \begin{eqnarray*} \dfrac{\partial u_{1}}{\partial t} & = & \mathit{k}_{1} (t) Δu_{1} + h_{1}(t) u_{1}^{…
Certain fractional Laplacian equations that do not have smooth solutions
José Villa-Morales
Let be a real-valued function defined on , with and which is not constant in non empty open intervals. We prove the equations \begin{equation}\label{e…
Solution of the Dirichlet problem for the equation by the Monte Carlo method
José Villa-Morales
In this paper we study the Dirichlet problem corresponding to an open bounded set and the operator \begin{equation*} A=\sum_{i=1}^{d}a\frac{\partial ^{2}}…
Global existence and persistence of mass for a nonlinear equation with fractional Laplacian
Eric Ruvalcaba-Robles, José Villa-Morales
In this paper we study the partial differential equation \begin{equation} \begin{split} \partial_tu &= k(t)Δ_αu - h(t)φ(u), u(0) &= u_0. \end{split} \end{equation} Here is th…
Existence of mild solutions for a system of partial differential equations with time-dependent generators
Amanda del Carmen Andrade-González, José Villa-Morales
We give sufficient conditions for global existence of positive mild solutions for the weak coupled system: \begin{eqnarray*} \frac{\partial u_{1}}{\partial t} &=&ρ_{1}t^{ρ_{1}-1}Δ_…
On the Distribution of Explosion Time of Stochastic Differential Equations
Jorge A. León, Liliana Peralta Hernández, José Villa-Morales
In this paper we use the Itô's formula and comparison theorems to study the blow-up in finite time of stochastic differential equations driven by a Brownian motion. In particular,…
Blow up of mild solutions of a system of partial differential equations with distinct fractional diffusions
José Villa-Morales
We give a sufficient condition for blow up of positive mild solutions to an initial value problem for a nonautonomous weakly coupled system with distinct fractional diffusions. The…