Nonlinear Nonlocal Equations in the Theory of Waves

Long‐time asymptotics of solutions of the second initial‐boundary valueproblem for the damped Boussinesq equation

“…n (t) with 0 ≤ s ≤ N − 1 we shall prove that it holds for s = N. Since for all integer n ≥ 1, q ≥ 1, n = q (see [14])…”

“…However, this technique does not work for a wide class of dissipative equations which are not completely integrable. Another approach has been proposed by Naumkin and Shishmarev [14], who have considered nonlocal evolution equations of the first order in time and with small initial data. By means of using both the spectral and perturbation theories they have succeeded in constructing the exact solutions of the Cauchy problems in question and have calculated their long-time asymptotics.…”

Critical Nonlinear Nonlocal Equations on a Half-Line

“…The theory of nonlinear pseudodifferential equations plays an important role in the contemporary mathematical physics(see book [11]). Such equations serve as a basis for mathematical models to describe the different phenomena in modern Physics, Biology, Technology and others fields of science.…”

Zero-Dissipation Limit for Nonlinear Waves

“…Numerous numerical simulations and analytical studies have been carried out to determine the effect of such a term in these models (cf. [4,7,8,12,13,15,16,21,[27][28][29]). Laboratory studies show (1.1) with p = 1 and a suitably chosen value of ν has good predictive power in cases where nonlinear effects are not too strong (e.g.…”