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Global well-posedness and attractors for the hyperbolic Cahn–Hilliard–Oono equation in the whole space (2016)
Journal Article
Savostianov, A., & Zelik, S. (2016). Global well-posedness and attractors for the hyperbolic Cahn–Hilliard–Oono equation in the whole space. Mathematical Models and Methods in Applied Sciences, 26(07), Article 1357. https://doi.org/10.1142/s0218202516500329

We prove the global well-posedness of the so-called hyperbolic relaxation of the Cahn–Hilliard–Oono equation in the whole space R3ℝ3 with the nonlinearity of the sub-quintic growth rate. Moreover, the dissipativity and the existence of a smooth globa... Read More about Global well-posedness and attractors for the hyperbolic Cahn–Hilliard–Oono equation in the whole space.

Attractors for Damped Quintic Wave Equations in Bounded Domains (2016)
Journal Article
Kalantarov, V., Savostianov, A., & Zelik, S. (2016). Attractors for Damped Quintic Wave Equations in Bounded Domains. Annales Henri Poincaré, 17(9), 2555-2584. https://doi.org/10.1007/s00023-016-0480-y

The dissipative wave equation with a critical quintic non-linearity in smooth bounded three-dimensional domain is considered. Based on the recent extension of the Strichartz estimates to the case of bounded domains, the existence of a compact global... Read More about Attractors for Damped Quintic Wave Equations in Bounded Domains.

Infinite energy solutions for critical wave equation with fractional damping in unbounded domains (2016)
Journal Article
Savostianov, A. (2016). Infinite energy solutions for critical wave equation with fractional damping in unbounded domains. Nonlinear Analysis: Theory, Methods and Applications, 136, 136-167. https://doi.org/10.1016/j.na.2016.02.016

This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of R3 with fractional damping of the form View the MathML source. The work extends previously known results for bounded domains in finite ener... Read More about Infinite energy solutions for critical wave equation with fractional damping in unbounded domains.