The asymptotic behavior of solutions for a class of doubly degenerate nonlinear parabolic equations (Q984756)

The author, by assuming the uniqueness of the Barenblatt-type solution (this result is not known in the general case), studies the large time asymptotic behavior of solutions for the doubly degenerate parabolic equation \[ u_t=\text{div}(|Du^m|^{p - 2}Du^m) - |Du^m|^{p_{1}} - u^q \] with initial condition \(u(x,0)= u_0(x)\). Where the exponents \(m,p,p_1,q\) satisfy \(p>p_1> p-1\), \(q>m(p-1)>1\), \(p>1\), \(m>1\).