Fraydoun Rezakhanlou (UC Berkeley)
Kinetic Theory for Hamilton-Jacobi PDEs
Hamilton-Jacobi PDEs with random stationary Hamiltonian functions are popular toy models for studying the dynamics of interfaces in various phenomena in physics and biology. There is a one-to-one correspondence between piecewise smooth solutions and marked tessellations. A kinetic theory can be developed to describe the dynamics of such tessellations. As an application, we find kinetically describable Gibbsian solutions for such PDEs.