Special Session #9

Modeling with Differential and Difference Equations with Uncertainties

Clara Burgos1, Juan Carlos Cortés1, Tomás Caraballo2, Gilberto González-Parra3, Javier López de la Cruz4, Rafael Villanueva1

1Universitat Politècnica de València, Spain, clabursi@posgrado.upv.es
1Universitat Politècnica de València, Spain, jccortes@imm.upv.es
2Universidad de Sevilla, Sevilla, Spain, caraball@us.es
3New Mexico Tech, New Mexico, USA, gilberto.gonzalezparra@nmt.edu
4Universidad Politécnica de Madrid, Madrid, Spain, javier.lopez.delacruz@upm.es
1Universitat Politècnica de València, Spain, rjvillan@imm.upv.es

The key role played by difference and differential equations in modeling the dynamics of physical problems (in a broad sense) is indisputable. Due to measurement errors of the quantities determining the input data (initial and/or boundary conditions, source terms and/or coefficients) of such equations, or simply to ignorance of the complexity of the phenomena under study, it is more realistic to formulate such difference and differential equations by means of appropriate random variables and/or stochastic processes. This new reformulation of classical differential (and its discrete counterpart) equations has given rise to different approaches to deal with differential equations with uncertainties ranging from the so-called stochastic differential equations to random differential equations, although other types of formulations, such as multi-valued differential equations have also been proposed. In addition to the interesting mathematical problems arising from the generalization of the classical theory to the stochastic/random/multivalued context, exciting new challenges appear from the point of view of mathematical modeling real problems, including the associated inverse problems for the choice of probability distributions for Uncertainty Quantification. This special session welcomes papers dealing with new advances in difference and differential equations with uncertainty and techniques for their application in mathematical modeling. Papers dealing with thorough discussions comparing the use of the aforementioned approaches using real-world data are particularly welcome..