A Laguerre expansion of the Cauchy problem for convective diffusive flow. (Q1399871)

The authors study the motion of reactants suspended in a bulk fluid and forced through a thin layer of catalyst held at the top of a long reactor column, taking into account the effects of a first-order convective term. This problem can be reduced to the solution of an inverse problem for a one-dimensional thermal convection-diffusion equation involving noncharacteristic Cauchy conditions. Using the inverse Laplace transform of a family of hyperbolic functions, the authors obtain the classical solution as a series expansion in Laguerre polynomials in time with spatial coefficients expressed in terms of a new set of special functions. The series solution is applied to investigate the well-posedness of the inverse problem.