Abstract
We study the well-posedness of renormalized entropy solutions for quasilinear anisotropic degenerate parabolic-hyperbolic equation of the type $\partial_{t}u+\text{div}f(u)=\nabla\cdot(a(u)\nabla u)$ in a bounded domain with general $L^{1}$ initial data and homogeneous Dirichlet boundary condition. We use the device of doubling variables to prove the uniqueness and use the vanishing viscosity method to prove the existence.
Citation
Yachun Li. Qin Wang. Zhigang Wang. "Renormalized entropy solutions of homogeneous Dirichlet problems for quasilinear anisotropic degenerate parabolic-hyperbolic equations." Adv. Differential Equations 19 (3/4) 387 - 408, March/April 2014. https://doi.org/10.57262/ade/1391109090
Information