Zobrazeno 1 - 10
of 70
pro vyhledávání: '"Sukhtayev, Alim"'
Autor:
Smith, Nathaniel, Sukhtayev, Alim
We derive a counting formula for the eigenvalues of Schr\"odinger operators with self-adjoint boundary conditions on quantum star graphs. More specifically, we develop techniques using Evans functions to reduce full quantum graph eigenvalue problems
Externí odkaz:
http://arxiv.org/abs/2402.07409
The Evans function is a well known tool for locating spectra of differential operators in one spatial dimension. In this paper we construct a multidimensional analogue as the modified Fredholm determinant of a ratio of Dirichlet-to-Robin operators on
Externí odkaz:
http://arxiv.org/abs/2206.07677
Autor:
Sukhtayev, Alim, Zumbrun, Kevin
Publikováno v:
In Journal of Functional Analysis 15 October 2024 287(8)
Autor:
Sukhtayev, Alim, Zumbrun, Kevin
Extending work of Carty, we show that $H^1$ solutions of a simplified 1D BGK model decay exponentially in $L^2$ to a subclass of the class of grossly determined solutions as defined by Truesdell and Muncaster. In the process, we determine the spectru
Externí odkaz:
http://arxiv.org/abs/2012.00734
Autor:
Howard, Peter, Sukhtayev, Alim
Working with a general class of linear Hamiltonian systems with at least one singular boundary condition, we show that renormalized oscillation results can be obtained in a natural way through consideration of the Maslov index associated with appropr
Externí odkaz:
http://arxiv.org/abs/2009.10681
It was recently shown by the authors that a semilinear elliptic equation can be represented as an infinite-dimensional dynamical system in terms of boundary data on a shrinking one-parameter family of domains. The resulting system is ill-posed, in th
Externí odkaz:
http://arxiv.org/abs/1907.10372
A characterization of a semilinear elliptic partial differential equation (PDE) on a bounded domain in $\mathbb{R}^n$ is given in terms of an infinite-dimensional dynamical system. The dynamical system is on the space of boundary data for the PDE. Th
Externí odkaz:
http://arxiv.org/abs/1907.09986
Autor:
Sukhtayev, Alim, Zumbrun, Kevin
We establish a Sturm{Liouville theorem for quadratic operator pencils counting their unstable real roots, with applications to stability of waves. Such pencils arise, for example, in reduction of eigenvalue systems to higher-order scalar problems.
Externí odkaz:
http://arxiv.org/abs/1907.05679
Autor:
Howard, Peter, Sukhtayev, Alim
We show that for Sturm-Liouville Systems on the half-line $[0,\infty)$, the Morse index can be expressed in terms of the Maslov index and an additional term associated with the boundary conditions at $x = 0$. Relations are given both for the case in
Externí odkaz:
http://arxiv.org/abs/1903.07583
By reduction to a generalized Sturm Liouville problem, we establish spectral stability of hydraulic shock profiles of the Saint-Venant equations for inclined shallow-water flow, over the full parameter range of their existence, for both smooth-type p
Externí odkaz:
http://arxiv.org/abs/1810.01490