Skew diffusion with drift : a new class of stochastic processes with applications to parabolic equations with piecewise smooth coefficients Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/m326m447p

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  • This thesis consists of three subsequent parts addressing the applications of stochastic processes to the analysis and solutions of parabolic equations with discontinuous coefficients that are of mathematical interest. The first two parts consist of three manuscripts, in which we analyze solutions of Fickian convection dispersion equations with discontinuous coefficients and provide mathematical treatment of solute transport across a sharp interface. We assume the dispersion coefficient is a piecewise constant across a plane (interface), the drift is constant and perpendicular to the interface. Also, assume the flux is continuous across the interface (interface condition). The transition probability density function of the underlying stochastic process, called skew diffusion with drift, is given. As an application, we obtain specific results to explain the interesting types of symmetries and asymmetries in the breakthrough curves of a conservative tracer across a sharp interface. Also, to answer an unsolved problem we give the first passage time density formula of skew Brownian motion. The third part is essentially an extension of the first two parts. In this part we analyze the stochastic processes associated with convection reaction-diffusion equations with discontinuous coefficients. The geometry of the interface and the condition at the interface considered here are more general than in the first two parts.
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  • description.provenance : Approved for entry into archive by Laura Wilson(laura.wilson@oregonstate.edu) on 2011-09-06T20:16:15Z (GMT) No. of bitstreams: 3 ArachchiAppuhamillageThilankaI2011.pdf: 921634 bytes, checksum: f42528a480cd56bb1aaa839f673f19a2 (MD5) license_rdf: 23484 bytes, checksum: c9bd6190935061f629979dd2c996fd05 (MD5) license_text: 21667 bytes, checksum: 961f5953d04b6704d3a5ad61eddd9f47 (MD5)
  • description.provenance : Made available in DSpace on 2011-09-06T20:16:15Z (GMT). No. of bitstreams: 3 ArachchiAppuhamillageThilankaI2011.pdf: 921634 bytes, checksum: f42528a480cd56bb1aaa839f673f19a2 (MD5) license_rdf: 23484 bytes, checksum: c9bd6190935061f629979dd2c996fd05 (MD5) license_text: 21667 bytes, checksum: 961f5953d04b6704d3a5ad61eddd9f47 (MD5) Previous issue date: 2011-08-11
  • description.provenance : Approved for entry into archive by Julie Kurtz(julie.kurtz@oregonstate.edu) on 2011-08-29T19:59:08Z (GMT) No. of bitstreams: 3 ArachchiAppuhamillageThilankaI2011.pdf: 921634 bytes, checksum: f42528a480cd56bb1aaa839f673f19a2 (MD5) license_rdf: 23484 bytes, checksum: c9bd6190935061f629979dd2c996fd05 (MD5) license_text: 21667 bytes, checksum: 961f5953d04b6704d3a5ad61eddd9f47 (MD5)
  • description.provenance : Submitted by Thilanka Arachchi Appuhamillage (arachcht@onid.orst.edu) on 2011-08-26T23:06:59Z No. of bitstreams: 3 ArachchiAppuhamillageThilankaI2011.pdf: 921634 bytes, checksum: f42528a480cd56bb1aaa839f673f19a2 (MD5) license_rdf: 23484 bytes, checksum: c9bd6190935061f629979dd2c996fd05 (MD5) license_text: 21667 bytes, checksum: 961f5953d04b6704d3a5ad61eddd9f47 (MD5)

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