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On stability of solutions for a nonclassical equation. (Russian. English summary) Zbl 1195.35050

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
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