Free boundary problems

Exact Methods for ODEs

Published in Daniel Zwillinger, Vladimir Dobrushkin, Handbook of Differential Equations, 2021

Daniel Zwillinger, Vladimir Dobrushkin

In free boundary problems, a differential equation must be solved in a domain whose size can vary. One of the unknowns to be determined is the size of the domain on which the equation is to be satisfied.

A free boundary problem for a class of nonlinear nonautonomous size-structured population model

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Journal Information

Published in Applicable Analysis, 2018

Wenbin Lv, Shaohua Wu

Free boundary problems deal with solving partial differential equations (PDEs) in a domain, a part of whose boundary is unknown in advance; that portion of the boundary is called a free boundary. In addition to the standard boundary conditions that are needed in order to solve the PDEs, an additional condition must be imposed at the free boundary. One then seeks to determine both the free boundary and the solution of the differential equations. The theory of free boundaries has seen great progress in the last century [1–3]. Recent decades have witnessed a rapid widening of the subject area by incorporation of important free boundary topics coming from different areas: in Finance, free boundary problems appear to determine the optimal exercise value in Black–Scholes models [4,5]; in Mathematical Biology, they indicate the moving fronts of populations or tumors [6–8].

Free boundary problems

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Exact Methods for ODEs

A free boundary problem for a class of nonlinear nonautonomous size-structured population model