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


76R99 Diffusion and convection
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
80A17 Thermodynamics of continua
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