Regularity and uniqueness of solutions to a parabolic system in nonequilibrium thermodynamics
The author deals with the parabolic system \[ {\partial \over\partial t}\rho_i(u)+ \text{div } J_i=W_i(u,V), \quad i=1,\ldots, n, \] \[ {\partial \over \partial t}\rho_{n+1}(u)+\text{div }J_{n+1}=W_{n+1}(u,V)- \sum_{k=1}^ne_k \nabla V\cdot J_k\quad \text{in} \Omega\times(0,\tau), \] where \(\Omega\subset \mathbb{R}^d\), \(d\geq 1\) is a bounded domain and \(\tau>0.\) Under suitable conditions on the data there are proved regularity \((u\in L^\infty(H^1)\cup H^1(L^2)\), \(V\in L^\infty(W^{2,p}))\) and uniqueness results.
scientific article; zbMATH DE number 1512501