The Cauchy problem for a two-component Hunter-Saxton equation, begin{align*}(u_t+uu_x)_x&=frac{1}{2}u_x^2+frac{1}{2}rho^2,rho_t+(urho)_x) &= 0,end{align*}on $mathbb{R}times[0,infty)$ is studied. Conservative and dissipative weak solutions are defined and shown to exist globally. This is done by explicitly solving systems of ordinary differential equation in the Lagrangian coordinates, and using these solutions to construct semigroups of conservative and dissipative solutions.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:ntnu-19057 |
| Date | January 2012 |
| Creators | Nordli, Anders Samuelsen |
| Publisher | Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, Institutt for matematiske fag |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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