Separation for the biharmonic differential operator in the Hilbert space associated with the existence and uniqueness theorem

Abstract

In this paper, we have studied the separation for the following biharmonic differential operator:is the space of all bounded linear operators on the Hilbert space H 1 and u is the biharmonic differential operator, while u = n i=1 ∂ 2 u ∂x 2 i is the Laplace operator in R n . Moreover, we have studied the existence and uniqueness of the solution of the biharmonic differential equationin the Hilbert space H , where f (x) ∈ H .

On coercive properties and separability of biharmonic operator with matrix potential

“…The separability of nonlinear second order differential operators with varying matrix coefficients in an -dimensional Euclidean space was studied before in work [11]. The present work generalizes work [9] for a nonlinear case.…”

“…Boimatov in work [5]. The separability of the linear biharmonic operator [ ] = ∆ 2 ( ) + ( ) ( ) was studied before in works [9], [10]. The separability of nonlinear second order differential operators with varying matrix coefficients in an -dimensional Euclidean space was studied before in work [11].…”

Pseudospectral meshless radial point interpolation for generalized biharmonic equation in the presence of Cahn–Hilliard conditions

“…Numerically solving this elliptic kind of partial differential equation becomes more important due to dual boundary conditions. The study of the existence and uniqueness of the solution of some kinds of biharmonic differential equations which are close to (1) have been done by many authors; see Reddy (1977); Zayed (2008); Karachik et al (2015) and references therein. Arad et al (1997) derived coefficients for a nine-point high-order accuracy discretization procedure for a biharmonic equation with simply supported and clamped boundary conditions.…”

Inequalities and Separation for a Biharmonic Laplace-Beltrami Differential Operator in a Hilbert Space Associated with the Existence and Uniqueness Theorem

“…Further results for separation of differential operators can be found in [22][23][24][25][26][27][28][29][30].…”