Functional solutions for problems of heat and mass transfer. (English) Zbl 1412.34238

Cimatti, Giovanni

Meccanica 54, No. 1-2, 7-18 (2019).

Summary: 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 \(\mathcal C_F=\mathcal C\).

MSC:

34L99	Ordinary differential operators
35J66	Nonlinear boundary value problems for nonlinear elliptic equations
80A20	Heat and mass transfer, heat flow (MSC2010)

Keywords:

mass and heat transfer; existence and uniqueness; two-point problem for O.D.E; systems of P.D.E in divergence form

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