Integrability and boundedness of local solutions to doubly degenerate quasilinear parabolic equations (Q5954426)

Let \(u(t,x)\) is a weak solution of the doubly degenerate quasilinear parabolic equation \(u_{t}-\text{div}(a(x,t,u,\nabla u))=b(x,t,u,\nabla u)\). Under some assumptions on the functions \(a,b,u\) the author obtains \(L_{q,\text{loc}}\) and \(L_{\infty ,\text{loc}}\) estimates for the local solution \(u.\)