The Bounded Solutions on a Semiaxis for the Linearized Hoff Equation in Quasi-Sobolev Spaces

Abstract

In this paper we investigate the properties of the linearized Hoff equation in quasi-Sobolev spaces. Hoff equation, specified on the interval, describes the buckling of the H-beam. Due to the fact that for certain values of the parameters in the equation may be missing the derivative with respect to time, this equation refers in a frame of class of nonclassical equations of mathematical physics. The article by relatively spectral theorem describes the morphology of the phase space and the existence of invariant spaces of solutions. Using these results, we prove the existence of bounded on the semiaxis solutions for homogeneous evolution equations of Sobolev type in quasi-Sobolev spaces. Apart of the introduction and bibliography the article contains three parts. The first one shows the results on the solvability of the investigated class of equations. The second part shows the existence of bounded on the semiaxis solutions for the homogeneous equations of the research class. Finally, the third part presents the results of the existence of solutions bounded on the semiaxis for analog linearized Hoff equation in quasi-Sobolev spaces.