This paper aims to construct conservation laws for a Benjamin–Bona–Mahony equation with variable coefficients, which is a third-order partial differential equation. This equation does not have a Lagrangian and so we transform it to a fourth-order partial differential equation, which has a Lagrangian. The Noether approach is then employed to construct the conservation laws. It so happens that th...

We are interested in the Gevrey properties of formal power series solution time inhomogeneous semilinear heat equation with a power-law nonlinearity $1$-dimensional variable $t\in\mathbb{C}$ and $n$-dimensional spatial $x\in\mathbb{C}^n$ analytic initial condition coefficients at origin $x=0$. prove particular that inhomogeneity together $s$-Gevrey for any $s\geq1$. In opposite case $s<1$, we s...

first riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. an analytical approximation of the solution of nonlinear differential riccati equation is investigated using the adomian decomposition method. an application in optimal control is presented. the solution in different order of approximations and different methods of approximat...