Strong solution for a mixed problem with nonlocal condition for certain pluriparabolic equations

A note on efficient techniques for the second-order parabolic equation subject to non-local conditions

“…We have chosen Eqs. (1)- (4), where now f (x) = exp(x), 0 < x < 1, g 1 (t) = 0, 0 < t < 1, g 2 (t) = e 1 + t 2 , 0 < t < 1, q(x, t) = exp(x)(1 + t) 2 (1 + t 2 ) 2 , 0 t 1, 0 < x < 1,…”

“…Several problems arising in thermodynamics [12,14,19], heat conduction [1,2], plasma physics [20] or inverse problems [21], can be reduced to the non-local problems with integral condition.…”

A meshless method for numerical solution of the one-dimensional wave equation with an integral condition using radial basis functions

“…This article used a functional analysis method based on an energy inequality and on the density of the range of the linear operator corresponding to the abstract formulation of the studied problem. We refer the interested reader to the nice papers of [1][2][3][4] for more research works in the theoretical aspects of the nonlocal models.…”

The method of lines for solution of the one-dimensional wave equation subject to an integral conservation condition

“…Growing attention is being paid to the development, analysis and implementation of numerical methods for the solution of these problems. Hyperbolic initial boundary value problems in one dimension that involve nonlocal boundary conditions have been studied by several authors [7,8,1,[9][10][11][12]. For parabolic equations subject to nonlocal boundary conditions the interested reader can see [13] and the references therein.…”