In this note we state a theorem which guarantees the existence and uniqueness of a global solution for the Cauchy initial value problem for a complete, regular system of partial differential equations of first order for one unknown function on a manifold—all data being of class C. This result depends on one hand on an investigation of the following problem for a w-dimensional C°°-manifold W, wh...

The Stefan PDE system is a representative model for thermal phase change phenomena, such as melting and solidification, arising in numerous science engineering processes. mathematical description given by Partial Differential Equation (PDE) of the temperature distribution defined on spatial interval with moving boundary, where boundary represents liquid–solid interface its dynamics are governed...

The paper presents an observer design for a class of hyperbolic PDE–ODE cascade systemswith a boundary measurement. The cascade systems consist of coupled PDEs, featuring one rightward and one leftward convecting first-order transport PDEs, and a set of ODEs, which enter the PDEs through the left boundary of the systems. The design, which is based on the Volterra integral transformation, relies...

A descrição da dinâmica dos sistemas físicos requer o detalhamento evolução das quantidades que os determinam ao passar de uma superfície tri-dimensional para outra, cada delas definida segundo parâmetro a é dado nome «tempo». Mas quais seriam essas superfícies e qual seria esse tempo escolha não única, senão diversa, como foi mostrado por Dirac em 1949; tais diferentes escolhas possíveis inequ...