Applied PDE Group
Nonlinear Partial Differential Equations in Fluid and Solid Mechanics

LT2013

Relative entropy in diffusive relaxation

​C. Lattanzio, A.E. Tzavaras, Relative entropy in diffusive relaxation, SIAM J. Math. Analysis 45 (2013), 1563-1584
C. Lattanzio, A.E. Tzavaras
relative entropy, diffusive relaxation, Euler equations
2013
​We establish convergence in the diffusive limit from entropy weak solutions of the equations of compressible gas dynamics with friction to the porous media equation away from vacuum. The result is based on a Lyapunov type of functional provided by a calculation of the relative entropy. The relative entropy method is also employed to establish convergence from entropic weak solutions of viscoelasticity with memory to the system of viscoelasticity of the rate type.