Shipilov, A. S. On stability of solutions for a nonclassical equation. (Russian. English summary) Zbl 1195.35050 Vestn. Yuzhno-Ural. Gos. Univ., Ser. Mat. Model. Program. 27(170), No. 4, 116-119 (2009). Summary: It is proved the existence of a finite-dimensional stable and an infinite dimensional unstable manifold for the equation \(\lambda u_t-u_{txx}=\nu u_{xx}- u_xu\), \(a\leq x\leq b\), with homogeneous Dirichlet boundary conditions. MSC: 35B35 Stability in context of PDEs 37L25 Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems 35G31 Initial-boundary value problems for nonlinear higher-order PDEs Keywords:Sobolev type equations; unstable and stable invariant manifolds; one space dimension; homogeneous Dirichlet boundary conditions PDFBibTeX XMLCite \textit{A. S. Shipilov}, Vestn. Yuzhno-Ural. Gos. Univ., Ser. Mat. Model. Program. 27(170), No. 4, 116--119 (2009; Zbl 1195.35050) Full Text: Link