Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in
Mechanics and Physics is the first book to provide a systematic construction of exact …

A self-contained introduction to the methods and techniques of symmetry analysis used to
solve ODEs and PDEs Symmetry Analysis of Differential Equations: An Introduction presents …

The dynamics of surface diffusion describes the motion of a surface with its normal velocity
given by the surface Laplacian of its mean curvature. This flow conserves the volume …

Micro-scale thermal interface grooving (TIG), as an important breakdown mechanism of
single lamella and the key to spheroidization of lamellar colony, does significant influence …

In this paper, we discuss the reduction to Fujita's equation for the nonlinear diffusion
equation under certain types of generalized conditional symmetry. It is shown that the …

This paper is concerned with two generalisations of the widely studied thin film equation
ut=−(unuxxx) x. Both are degenerate fourth-order parabolic equations in conservation form; …

Abstract Changes in morphology of a polycrystalline material may occur through interface
motion under the action of a driving force. An important special case that is considered in …

Given a Lie group acting on a manifold, our aim is to analyze the evolution of differential
invariants under invariant submanifold flows. The constructions are based on the equivariant …

In a previous paper, we solved the partial differential equation of Mullins' problem in the
case of the evaporation–condensation in electronic devices and gave an exact solution …

purpose. In glaucoma, elevated intraocular pressure causes a progressive loss of retinal
ganglion cells and results in optic neuropathy. The authors propose a potential mechanism …