, Volume 54, Issue 1–2, pp 7–18 | Cite as

Functional solutions for problems of heat and mass transfer

  • Giovanni CimattiEmail author


We prove the existence and, in certain cases, the uniqueness of functional solutions for boundary value problems of systems of P.D.E. in divergence form with constant boundary conditions. We are motivated by various problems of heat and mass transfer. After giving a suitable definition of functional solutions, we reformulate the boundary value problem as non-standard one-dimensional two point problem for a system of O.D.E coupled with a mixed problem for the laplacian. If \({{{\mathcal {C}}}}_F\) and \({{{\mathcal {C}}}}\) denote respectively the set of functional and classical solutions of the starting problem we settle, in simple cases, the question if \({{{\mathcal {C}}}}_F={{{\mathcal {C}}}}\).


Mass and heat transfer Existence and uniqueness Two-point problem for O.D.E Systems of P.D.E in divergence form 

Mathematics Subject Classification

34L99 35J66 



Several pertinent and useful suggestions of the Referees are gratefully acknowledged.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of PisaPisaItaly

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