Search results for " Lie symmetries"
showing 2 items of 2 documents
A group analysis via weak equivalence transformations for a model of tumor encapsulation
2004
A symmetry reduction of a PDEs system, describing the expansive growth of a benign tumour, is obtained via a group analysis approach. The presence in the model of three arbitrary functions suggests the use of Lie symmetries by using the weak equivalence transformations. An invariant classification is given which allows us to reduce the initial PDEs system to an ODEs system. Numerical simulations show a realistic enough description of the physical process.
On a radiating fluid in a general relativistic context
2006
A model for the radiation hydrodynamics in general relativity is analyzed, describing the gravitational collapse and supernovae explosion. As these physical phenomena can be assumed spherically symmetric, the equations of motion for a unique fluid, representing the interaction between matter and radiation, are written in a spherical symmetric space-time with respect to a comoving frame. The system is completed by using the Eddington closure, assuming a local thermodynamical equilibrium for the radiation field. The resulting system is analyzed by the Lie symmetry approach and a reduction to an ODEs system is obtained. Numerical simulations of the solutions are performed, showing a realistic …