Global existence for nonlinear parabolic equations with a damping term
The authors prove the global existence of positive and bounded weak solutions to the equation \(\partial_t u -\text{div}(a(x,t,u,\nabla u)) + C|\nabla u|^\nu = g(u)\) (in a bounded and open domain) with an exponent \(\nu\in (1,2]\), a function \(a\) satisfying suitable ellipticity and growth conditions, a locally Lipschitzian function \(g\), and a sufficiently large damping constant \(C>0\).
scientific article; zbMATH DE number 5546288