16 citations · 29 across the 8 of their papers we have counts for
10 papers
Infinite energy solutions for weakly damped quintic wave equations in
Xinyu Mei, Anton Savostianov, Chunyou Sun +1
The paper gives a comprehensive study of infinite-energy solutions and their long-time behavior for semi-linear weakly damped wave equations in with quintic nonlinea…
Uniform attractors for measure-driven quintic wave equation with periodic boundary conditions
Anton Savostianov, Sergey Zelik
We give a detailed study of attractors for measure driven quintic damped wave equations with periodic boundary conditions. This includes uniform energy-to-Strichartz estimates, the…
Homogenisation with error estimates of attractors for damped semi-linear anisotropic wave equations
Shane Cooper, Anton Savostianov
Homogenisation of global and exponential attractors for the damped semi-linear anisotropic wave equation $\partial_t^2 u^ε+γ\partial_t u^ε-{\rm div}…
Infinite energy solutions for critical wave equation with fractional damping in unbounded domains
Anton Savostianov
This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of with fractional damping of the form $(-Δ_x+1)^\frac{1}…
Finite Dimensionality of the attractor for the hyperbolic Cahn-Hilliard-Oono Equation in R^3
Anton Savostianov, Sergey Zelik
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 started in our pre…
Global well-posedness and attractors for the hyperbolic Cahn-Hilliard-Oono equation in the whole space
Anton Savostianov, Sergey Zelik
We prove the global well-posedness of the so-called hyperbolic relaxation of the Cahn-Hilliard-Oono equation in the whole space R^3 with the non-linearity of the sub-quintic growth…
Strichartz estimates and smooth attractors for a sub-quintic wave equation with fractional damping in bounded domains
Anton Savostianov
The work is devoted to Dirichlet problem for sub-quintic semi-linear wave equation with damping damping term of the form , , in bounded smo…
Recent progress in attractors for quintic wave equations
Anton Savostianov, Sergey Zelik
We report on new results concerning the global well-posedness, dissipativity and attractors of the damped quintic wave equations in bounded domains of R^3.
Attractors for damped quintic wave equations in bounded domains
Varga Kalantarov, Anton Savostianov, Sergey Zelik
The dissipative wave equation with a critical quintic nonlinearity in smooth bounded three dimensional domain is considered. Based on the recent extension of the Strichartz estimat…
Smooth attractors for the quintic wave equations with fractional damping
Anton Savostianov, Sergey Zelik
Dissipative wave equations with critical quintic nonlinearity and damping term involving the fractional Laplacian are considered. The additional regularity of energy solutions is e…