{"id":{"repo_id":"unr","oai_identifier":"oai:scholarwolf.unr.edu:11714/3679"},"canonical_url":"https://search.dev.ndltd.org/etd/unr/oai:scholarwolf.unr.edu:11714/3679","repository":{"repo_id":"unr","name":"University of Nevada - Reno","base_url":"https://scholarwolf.unr.edu/server/oai/request"},"display":{"title":"A Series Solution to the Porous Medium Equation","abstract":"The Porous Medium Equation is a generalization of the Boussinesqequation, when the diffusivity is a power-law function of thehydraulic head, not only a linear function as in the case of theBoussinesq equation. We consider the case of a one-dimensionalaquifer, initially dry, and of semi-infinite extent. At theboundary representing a fluid source, the boundary condition isspecified as a power-law function of time. Following Barenblatt'sapproach, self-similar variables can be introduced. This reducesthe original initial-boundary value problem for the partialdifferential equation to a boundary value problem for a nonlinearordinary differential equation. The boundary representing thewetting front is not known, and must be found in the process ofsolution. A power series solution is found for this nonlinear ODE.We construct a recurrence relation for the coefficients of theseries, and show the convergence of the series. Results arecompared against a highly accurate numerical solution of this ODEas well as the results of a lab-scale experiment.","abstract_html":"The Porous Medium Equation is a generalization of the Boussinesqequation, when the diffusivity is a power-law function of thehydraulic head, not only a linear function as in the case of theBoussinesq equation. We consider the case of a one-dimensionalaquifer, initially dry, and of semi-infinite extent. At theboundary representing a fluid source, the boundary condition isspecified as a power-law function of time. Following Barenblatt'sapproach, self-similar variables can be introduced. This reducesthe original initial-boundary value problem for the partialdifferential equation to a boundary value problem for a nonlinearordinary differential equation. The boundary representing thewetting front is not known, and must be found in the process ofsolution. A power series solution is found for this nonlinear ODE.We construct a recurrence relation for the coefficients of theseries, and show the convergence of the series. Results arecompared against a highly accurate numerical solution of this ODEas well as the results of a lab-scale experiment.","abstract_has_math":false,"creators":["Furtak-Cole, Eden"],"institution":null,"degree_name":null,"degree_level":"Master's Degree","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Telyakovskiy, Aleksey S."],"committee_chairs":[],"committee_members":["Mortensen, Jeff","Cooper, Clay"],"year":2012,"date_issued":"2012","date_published":"2012","updated_at":"2026-07-27T21:45:57Z","subjects":["Dimensional Analysis","Numerical Solution","ODE","PDE","PME","Power Series"],"languages":[],"rights":["In Copyright(All Rights Reserved)"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11714/3679","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Telyakovskiy, Aleksey S."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Mortensen, Jeff","Cooper, Clay"]},{"key":"dc:creator","label":"Author","values":["Furtak-Cole, Eden"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-07-26T18:23:44Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2018-07-26T18:23:44Z"]},{"key":"dc:date.issued","label":"Date","values":["2012"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's Degree"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Dimensional Analysis","Numerical Solution","ODE","PDE","PME","Power Series"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright(All Rights Reserved)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11714/3679"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The Porous Medium Equation is a generalization of the Boussinesqequation, when the diffusivity is a power-law function of thehydraulic head, not only a linear function as in the case of theBoussinesq equation. We consider the case of a one-dimensionalaquifer, initially dry, and of semi-infinite extent. At theboundary representing a fluid source, the boundary condition isspecified as a power-law function of time. Following Barenblatt'sapproach, self-similar variables can be introduced. This reducesthe original initial-boundary value problem for the partialdifferential equation to a boundary value problem for a nonlinearordinary differential equation. The boundary representing thewetting front is not known, and must be found in the process ofsolution. A power series solution is found for this nonlinear ODE.We construct a recurrence relation for the coefficients of theseries, and show the convergence of the series. Results arecompared against a highly accurate numerical solution of this ODEas well as the results of a lab-scale experiment."]},{"key":"dc:format","label":"Dc Format","values":["PDF"]},{"key":"dc:title","label":"Title","values":["A Series Solution to the Porous Medium Equation"]}]}],"canonical_facts":{"dc:contributor.advisor":["Telyakovskiy, Aleksey S."],"dc:contributor.committeemember":["Mortensen, Jeff","Cooper, Clay"],"dc:creator":["Furtak-Cole, Eden"],"dc:date.accessioned":["2018-07-26T18:23:44Z"],"dc:date.available":["2018-07-26T18:23:44Z"],"dc:date.issued":["2012"],"dc:description.abstract":["The Porous Medium Equation is a generalization of the Boussinesqequation, when the diffusivity is a power-law function of thehydraulic head, not only a linear function as in the case of theBoussinesq equation. We consider the case of a one-dimensionalaquifer, initially dry, and of semi-infinite extent. At theboundary representing a fluid source, the boundary condition isspecified as a power-law function of time. Following Barenblatt'sapproach, self-similar variables can be introduced. This reducesthe original initial-boundary value problem for the partialdifferential equation to a boundary value problem for a nonlinearordinary differential equation. The boundary representing thewetting front is not known, and must be found in the process ofsolution. A power series solution is found for this nonlinear ODE.We construct a recurrence relation for the coefficients of theseries, and show the convergence of the series. Results arecompared against a highly accurate numerical solution of this ODEas well as the results of a lab-scale experiment."],"dc:format":["PDF"],"dc:identifier.uri":["http://hdl.handle.net/11714/3679"],"dc:rights":["In Copyright(All Rights Reserved)"],"dc:subject":["Dimensional Analysis","Numerical Solution","ODE","PDE","PME","Power Series"],"dc:title":["A Series Solution to the Porous Medium Equation"],"dc:type":["Thesis"],"thesis:degree_level":["Master's Degree"]},"updated_at":"2026-07-27T21:45:57Z"}