Environmental concerns are driving the development of the welding processes and applications

In our model we take into account only diffusion and velocity of chemical reaction near the surface of the crystal and suggest applying non-linear reaction-diffusion equation with

Classical Sturm oscillation theory states that the number of oscillations of the fundamental solutions of a regular Sturm-Liouville equation at energy E and over a (possibly

We prove that for some form of the nonlinear term these simple modes are stable provided that their energy is large enough.. Here stable means orbitally stable as solutions of

In this article we consider the problem of unique continuation for high-order equations of Korteweg-de Vries type which include the kdV hierarchy.. It is proved that if the difference

We will study the spreading of a charged microdroplet using the lubrication approximation which assumes that the fluid spreads over a solid surface and that the droplet is thin so

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