Series solution of the Smoluchowski’s coagulation equation

On the Fundamental Solution of a Linearized Homogeneous Coagulation Equation

We describe the fundamental solution of the equation that is obtained by linearization of the coagulation equation with kernel K (x, y) = (xy)λ/2, around the steady state f (x) = x−(3+λ)/2 with λ ∈ (1, 2). Detailed estimates on its asymptotics are obtained. Some consequences are deduced for the flux properties of the particles distributions described by such models.

Neumann-Series Solution of Fractional Differential Equation

Neumann Series Analysis of the Wigner Equation Solution

The existence and uniqueness of the electron transport Wigner equation solution, determined by boundary conditions, is analyzed in terms of the Neumann series expansion of the integral form of the equation, obtained with the help of Newton’s trajectories. For understanding of the peculiarities of Wigner-quantum electron transport in semiconductor structures such mathematical issues can not be s...

a cross-comparative dtudy between two textbook series in terms of the presentation of politeness

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Psi-series solution of fractional Ginzburg–Landau equation

One-dimensional Ginzburg–Landau equations with derivatives of noninteger order are considered. Using psi-series with fractional powers, the solution of the fractional Ginzburg–Landau (FGL) equation is derived. The leading-order behaviours of solutions about an arbitrary singularity, as well as their resonance structures, have been obtained. It was proved that fractional equations of order α wit...