Katya Dimova, Rita Meyer-Spasche
IDS GmbH Analysis and Reporting Services
A Company of Allianz, München, D-80802, GERMANY
e-mail: katyadimova@yahoo.com
MPI for Plasma Physics
EURATOM Association
Garching bei München, D-85748, GERMANY
e-mail: meyer-spasche@ipp.mpg.de

Abstract.One of the main problems in fusion research is to understand the dynamics of heat transport in a tokamak plasma. In certain scenarios the heat flux suddenly is much larger than predicted by classical theory, ``anomalously'' large. In this paper we investigate a mathematical model for the onset of ``anomalous transport'' as suggested by measurements in tokamaks.

We consider a quasilinear heat equation with a heat conduction coefficient that depends piecewise linearly on the gradient of the temperature. The local non-differentiability of the coefficient gives rise to a moving front. Assuming a solution given, we investigate its smoothness and the properties of the front. Also, an ODE for the velocity of the front is derived, which leads to a front tracking technique. Then we prove existence of a unique solution, under assumptions suggested by the investigation of the front. We also give two families of parameter dependent exact solutions.

Received: September 9, 2008

AMS Subject Classification: 35K55, 35B65, 35R35

Key Words and Phrases: quasilinear heat equation, generalized solution, moving free boundary, front tracking, plasma physics

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 47
Issue: 4