A three-point boundary value problem with an integral condition for parabolic equations with the Bessel operator

Abstract

We prove the existence and uniqueness of a strong solution for a linear third-order equation with integral boundary conditions. The proof uses energy inequalities and the density of the range of the generated operator.

An Integral Two Space-Variables Condition for Parabolic Equations

“…Boundary-value problems for parabolic equations with integral boundary condition are investigated by Batten (1963); Bouziani and Benouar (1998); Cannon (1963);(1984); Cannon et al (1987); Ionkin (1977); Kamynin (1964); Field and Komkov (1992); Shi (1993); Marhoune and Bouzit (2005); Marhoune and Hameida (2008); Denche et al (1994); Denche and Marhoune (2001); Marhoune and Latrous (2008); Yurchuk (1986) and many references therein. The problem with integral one space-variable (respectively two space-variables) condition is studied in Fairweather and Saylor (1991) and Denche and Marhoune (2000) (respectively in Marhoune (2007) and Marhoune and Lakhal (2009)).…”

Strong solution for a high order boundary value problem with integral condition

“…We remark that integral boundary conditions for evolution problems have various applications in chemical engineering, thermoelasticity, underground water flow and population dynamics; see for example [7,12,22,17]. Boundary value problems for parabolic equations with an integral boundary condition are investigated by Batten [1], Bouziani and Benouar [2], Cannon [4,5], Cannon, et al [6], Ionkin [15], Kamynin [16], Shi and Shillor [23], Shi [22], Marhoune and Bouzit [19], Denche and Marhoune [8,9,10,11], Yurchuk [24], and many references therein. The problem with an integral one-space-variable condition is studied in Kartynnik [17], and Denche and Marhoune [11]…”

A numerical solution to nonlinear multi-point boundary value problems in the reproducing kernel space

“…They arise in the mathematical modeling of viscoelastic and inelastic flows, deformation of beams and plate deflection theory. In recent years, much attention has been given to solving the multi‐point boundary value problems 1–3. Several numerical and analytical techniques are being developed for solving these problems 1, 4–8.…”