Long-term analysis of degenerate parabolic equations in \(\mathbb R^N\)
The authors establish that the solution semigroup of \[ \partial_t u-\sum_{i=1}^N\partial_{x_i}\bigl(\left| \partial_{x_i}\right|^{p-2}\partial_{x_i}\bigr)+f(u)=g(x), \qquad x\in{\mathbb R}^N \] has a \((L^2_U({\mathbb R}^N),L^2_{\text{loc}}({\mathbb R}^N))\)-global attractor in case that \(p>2\), \(g\in L^2_U({\mathbb R}^N)\), \(f\in C({\mathbb R}^N,{\mathbb R}^N)\), \(f(0)=0\), \(f\) has polynomial growth, and satisfies certain local Lipschitz-type and monotonicity-type conditions. They also give an estimate for the Kolmogorov \(\epsilon\)-entropy of the attractor. The work is based on the \(l\)-trajectory method.
scientific article; zbMATH DE number 6419645
scientific article