that of isotropic media, the two equations coincide to a single second-order equation
, whence the medium appears free of birefringence [4,7-10].
These kinetic models included the pseudo first-order equation, the pseudo second-order equation
and the Elovich equation.
Figure 3 shows conversion rate predicted basing on the second-order equation
and variable order calculated by Eq.
The sorption process could be best described by the second-order equation
can be transformed into a second-order equation
Canonical forms are discussed for the linear second-order equation
, along with the Cauchy problem, existence and uniqueness of solutions, and characteristics as carriers of discontinuities in solutions.
They cover linear and nonlinear problems and discuss first-order scalar linear and nonlinear ordinary differential equations, second-order ordinary differential equations and damped oscillations, boundary-value problems, eigenvalues of linear boundary-value problems, variable coefficients and adjoints, resonance, second-order equations
in the phase plane, systems of equations, the fundamental existence theorem, random functions, chaos, linear systems and linearization, stable and unstable fixed points, multiple solutions for nonlinear boundary-value problems, bifurcation, continuation and path-following, periodic ordinary differential equations, boundary and interior layers, the complex plane, and time-dependent partial differential equations.
Author of "Cosmology in generalized Homdeski theories with second-order equations
cj] in ascending order of [delta], the second-order equations
are nonlinear, but the solutions are available by using elliptic functions.
They cover second-order equations
modeling stationary MEMS, parabolic equations modeling MEMS dynamic deflection, and fourth-order equations modeling non-elastic MEMS.
After introducing the strong limit-point and strong limit-circle properties of solutions, the authors consider second-order equations
with damping terms, higher order equations, second-order delay differential equations, and the use of transformations in obtaining nonlinear solutions.
He covers first-order equations, linear second-order equations
, elements of Fourier analysis, the wave equation, the heat equation, Dirichlet and Neumann problems, existence theorems, and a selection of the aforesaid advanced topics.