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Existence and uniqueness in nonclassical diffusion. (English) Zbl 0651.76040
Existence and uniqueness results for the solution of initial-boundary value problems for evolution type fourth order (in the space variables) partial differential equations are reported. The equations, referred to as nonclassical diffusion equations, are obtained from thermodynamic considerations discussed elsewhere. In some aspects (stationary processes, in particular) they remind one of the classical equations of linear elasticity.
Reviewer: N.Vulchanov
MSC:
76R99Diffusion and convection (fluid mechanics)
35G10Initial value problems for linear higher-order PDE
35K25Higher order parabolic equations, general
80A17Thermodynamics of continua