Global Solutions for a Free Boundary Problem of Hyperbolic Type in the Case of Non-negative Peeling Speed

Kazuaki Nakane () and Tomoko Shinohara ()
Additional contact information
Kazuaki Nakane: Faculty of Engineering, Osaka Institute of Technology
Tomoko Shinohara: Kyoto University, Faculty of Integrated Human Studies

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2003, pp 755-764 from Springer

Abstract: Abstract Let us consider the following one-dimensional free boundary problem $$ (P)\left\{ {\begin{array}{*{20}{c}} {{{u}_{{xx}}} - {{u}_{{tt}}} = 0\quad in\quad (0,\infty ) \times \{ t > 0\} \cap \{ u > 0\} ,} \hfill \\ {u_{x}^{2} - u_{t}^{2} = {{Q}^{2}}\quad on\quad (0,\infty ) \times \{ t > 0\} \cap \partial \{ u > 0\} ,} \hfill \\ \end{array} } \right. $$ with the initial conditions $$ (I)\left\{ {\begin{array}{*{20}{c}} {u(x,0) = e(x)\quad on\quad ( - {{l}_{0}},0),} \\ {{{u}_{t}}(x,0) = g(x)\quad on\quad ( - {{l}_{0}},0),} \\ \end{array} } \right. $$ and the boundary condition $$ (B)\quad u( - {{l}_{0}},t) = f(t)\quad on\quad [0,\infty ), $$ where e(x), g(x) and f(t) are given functions, Q and l 0 are positive constants.

Keywords: Unique Solution; Free Boundary; Global Solution; Global Existence; Free Boundary Problem (search for similar items in EconPapers)
Date: 2003
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55711-8_71

Ordering information: This item can be ordered from
http://www.springer.com/9783642557118

DOI: 10.1007/978-3-642-55711-8_71

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().