Outputs (2)

Finite dimensionality of the attractor for the hyperbolic Cahn-Hilliard-Oono equation in R3 (2015)
Journal Article
Savostianov, A., & Zelik, S. (2016). Finite dimensionality of the attractor for the hyperbolic Cahn-Hilliard-Oono equation in R3. Mathematical Methods in the Applied Sciences, 39(5), 1254-1267. https://doi.org/10.1002/mma.3569

In this paper, we continue the study of the hyperbolic relaxation of the Cahn–Hilliard–Oono equation with the sub-quintic non-linearity in the whole space math formula started in our previous paper and verify that under the natural assumptions on the... Read More about Finite dimensionality of the attractor for the hyperbolic Cahn-Hilliard-Oono equation in R3.

Strichartz estimates and smooth attractors for a sub-quintic wave equation with fractional damping in bounded domains (2015)
Journal Article
Savostianov, A. (2015). Strichartz estimates and smooth attractors for a sub-quintic wave equation with fractional damping in bounded domains. Advances in differential equations, 20(5/6), 495-530

The work is devoted to Dirichlet problem for sub-quintic semi-linear wave equation with damping term of the form (−Δx)α∂tu(−Δx)α∂tu, α∈(0,12)α∈(0,12), in bounded smooth domains of R3R3. It appears that to prove well-posedness and develop smooth attra... Read More about Strichartz estimates and smooth attractors for a sub-quintic wave equation with fractional damping in bounded domains.