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Journal of Applied Mathematics and Statistical Applications | Volume: 1
August 23-24, 2018 | London, UK
Applied Physics
3
rd
International Conference on
Novelties in additive manufacturing and bio-printing
Carey Caginalp
University of Pittsburgh, USA
N
onlinear conservation laws subject to random initial
conditions pose fundamental problems in the evolution
and interactions of shocks and rarefactions. Using a discrete
set of values for the solution, we derive a hierarchy of
equations in terms of the states in two differentmethods. This
hierarchy involves the n-point function, the probability that
the solution takes on various values at different positions, in
terms of the n+ 1-point function. In the first approach, these
equations can be closed but the resulting solutions do not
persist through shock interactions. In our second approach,
the n-point function is expressed in terms of the n+ 1-point
functions, and remains valid through collisions of shocks.
e:
carey_caginalp@alumni.brown.edu