Local well-posedness for thermodynamically motivated quasilinear parabolic systems in divergence form
- Druet, Pierre-Étienne
2010 Mathematics Subject Classification
- 35K40 35K51 35K57, 35K59, 35D35, 35B65
- doubly nonlinear parabolic system, advection--diffusion--reaction equations, a-priori estimates, local--in--time existence and uniqueness, classical solutions
We show that fully quasilinear parabolic systems are locally well posed in the Hilbert space scala if the coefficients of the differential operator are smooth enough and the spatial domain is sufficiently regular. In the context of diffusion systems driven by entropy, the uniform parabolicity follows from the second law of thermodynamics.