A non-classical initial and boundary value problem for a non-homogeneous one-dimensional heat equation for a semi-infinite material with a zero temperature boundary condition is studied. It is not a standard heat conduction ...

We consider the non-classical heat equation in the n-dimensional domain D = R+ × Rn−1 for which the internal energy supply depends on the heat flux on the boundary S = ∂D. The problem is motivated by the modeling of ...

We establish in this paper the equivalence between a Volterra integral equation of the second kind and a singular ordinary differential equation of the third order with two initial conditions and an integral boundary ...

A non-classical one dimensional Stefan problem with thermal coefficients temperature dependent and a Robin type condition at fixed face x=0 for a semi-infinite material is considered. The source function depends on the ...

In this work, studies of two-dimensional transient heat diffusion problems in domains of rectangular and elliptical geometries, submitted to boundary conditions of first kind, were carried out. For the problem formulation, ...

The mathematical analysis of two one-phase unidimensional and non-classical Stefan problems with nonlinear thermal coecients is obtained. Two related cases are considered, one of them has a temperature condition on the ...

The classic conservative approach for thermal process design can lead to over-processing, especially for laminar flow, when a significant distribution of temperature and of residence time occurs. In order to optimize quality ...

We consider a charged Brownian particle bounded by an harmonic potential, embedded in a Markovian heat bath and driven from equilibrium by external electric and magnetic fields. We develop a quaternionic-like (or Pauli ...

Let Omega be a smooth bounded domain in R-n, n >= 5. We consider the classical semilinear heat equation at the critical Sobolev exponent. ut =Delta u + un+2/n-2 in Omega x (0, infinity), u = 0 on partial derivative Omega ...