Kuttler, K.; Aifantis, Elias C. Existence and uniqueness in nonclassical diffusion. (English) Zbl 0651.76040 Q. Appl. Math. 45, 549-560 (1987). 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 Cited in 18 Documents MSC: 76R99 Diffusion and convection 35G10 Initial value problems for linear higher-order PDEs 35K25 Higher-order parabolic equations 80A17 Thermodynamics of continua Keywords:evolution equation; Existence; uniqueness results; initial-boundary value problems; nonclassical diffusion equations PDFBibTeX XMLCite \textit{K. Kuttler} and \textit{E. C. Aifantis}, Q. Appl. Math. 45, 549--560 (1987; Zbl 0651.76040) Full Text: DOI