Exact analytic solutions of the porous media and the gas pressure diffusion ODEs in non-linear mechanics

Panayotounakos, DE; Sotiropoulou, AB; Sotiropoulos, NB; Manios, M

dc.contributor.author	Panayotounakos, DE	en
dc.contributor.author	Sotiropoulou, AB	en
dc.contributor.author	Sotiropoulos, NB	en
dc.contributor.author	Manios, M	en
dc.date.accessioned	2014-03-01T01:26:19Z
dc.date.available	2014-03-01T01:26:19Z
dc.date.issued	2007	en
dc.identifier.issn	0020-7462	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18009
dc.subject	Exact analytic solutions	en
dc.subject	Gas pressure diffusion equation	en
dc.subject	Kidder's equation	en
dc.subject	Non-linear ODEs	en
dc.subject.classification	Mechanics	en
dc.subject.other	Function evaluation	en
dc.subject.other	Mathematical transformations	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Ordinary differential equations	en
dc.subject.other	Problem solving	en
dc.subject.other	Abel's equations	en
dc.subject.other	Gas pressure diffusion equations	en
dc.subject.other	Kidder's equation	en
dc.subject.other	Mathematical physics	en
dc.subject.other	Nonlinear mechanics	en
dc.subject.other	Porous materials	en
dc.title	Exact analytic solutions of the porous media and the gas pressure diffusion ODEs in non-linear mechanics	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ijnonlinmec.2006.10.018	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ijnonlinmec.2006.10.018	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	Two kinds of second-order non-linear ordinary differential equations (ODEs) appearing in mathematical physics and non-linear mechanics are analyzed in this paper. The one concerns the Kidder equation in porous media and the second the gas pressure diffusion equation. Both these equations are strongly non-linear including quadratic first-order derivatives (damping terms). By a series of admissible functional transformations we reduce the prescribed equations to Abel's equations of the second kind of the normal form that they do not admit exact analytic solutions in terms of known (tabulated) functions. According to a mathematical methodology recently developed concerning the construction of exact analytic solutions of the above class of Abel's equations, we succeed in performing the exact analytic solutions of both Kidder's and gas pressure diffusion equations. The boundary and initial data being used in the above constructions are in accordance with each specific problem under considerations. (C) 2007 Published by Elsevier Ltd.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	International Journal of Non-Linear Mechanics	en
dc.identifier.doi	10.1016/j.ijnonlinmec.2006.10.018	en
dc.identifier.isi	ISI:000246644400013	en
dc.identifier.volume	42	en
dc.identifier.issue	1	en
dc.identifier.spage	157	en
dc.identifier.epage	163	en