arXiv subjects

V. K. Kalantarov

Publications and source records attributed to V. K. Kalantarov.

4 recordsLinked to original sources

arXiv2026

Stabilization of the Marine Riser model by controllers depending on finitely many parameters

We prove global stabilization of the marine riser models using a feedback controller that depend on finitely many finite-volume elements and finitely many nodal observables. Our approach is based on a feedback control design for dissipative nonlinear partial differential equations, inspired by the methodology introduced in [Evol. Equ. Control Theory, Vol. 3 (2014), 579-594]. The proposed control strategy ensures asymptotic stabilization while maintaining computational feasibility, making it suitable for practical applications.

math.OC↗

arXiv2015

About Blow up of Solutions With Arbitrary Positive Initial Energy to Nonlinear Wave Equations

We show that blow up of solutions with arbitrary positive initial energy of the Cauchy problem for the abstract wacve eqation of the form $Pu_{tt}+Au=F(u) \ (*)$ in a Hilbert space, where $P,A$ are positive linear operators and $F(\cdot)$ is a continuously differentiable gradient operator can be obtained from the result of H.A. Levine on the growth of solutions of the Cauchy problem for (*). This result is applied to the study of inital boundary value problems for nonlinear Klein-Gordon equations, generalized Boussinesq equations and nonlinear plate equations. A result on blow up of solutions with positive initial energy of the initial boundary value problem for wave equation under nonlinear boundary condition is also obtained.

math.AP↗

arXiv2012

Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials

We study initial boundary value problems for the convective Cahn-Hilliard equation $\Dt u +\px^4u +u\px u+\px^2(|u|^pu)=0$. It is well-known that without the convective term, the solutions of this equation may blow up in finite time for any $p>0$. In contrast to that, we show that the presence of the convective term $u\px u$ in the Cahn-Hilliard equation prevents blow up at least for $0<p<\frac49$. We also show that the blowing up solutions still exist if $p$ is large enough ($p\ge2$). The related equations like Kolmogorov-Sivashinsky-Spiegel equation, sixth order convective Cahn-Hilliard equation, are also considered.

math.AP↗

arXiv2010

Infinite energy solutions for the Cahn-Hilliard equation in cylindrical domains

We give a detailed study of the infinite-energy solutions of the Cahn-Hilliard equation in the 3D cylindrical domains in uniformly local phase space. In particular, we establish the well-posedness and dissipativity for the case of regular potentials of arbitrary polynomial growth as well as for the case of sufficiently strong singular potentials. For these cases, we prove the further regularity of solutions and the existence of a global attractor. For the cases where we have failed to prove the uniqueness (e.g., for the logarithmic potentials), we establish the existence of the trajectory attractor and study its properties.

math.AP↗