A Class of Singular Perturbation Problem for the Nonlinear Differential-Integral Disturbed Evolution Equation

A Class of Shock Wave Solution to Singularly Perturbed Nonlinear Time-Delay Evolution Equations

“…For convenience, we still substitute u ij for u ij below. en, from equation (34), we have the boundary corrective term U near 0 ≤ ρ ≤ ρ 0 .…”

“…Substituting equations ( 14), ( 22), (34), and (46) into equations ( 42)-(45), expanding nonlinear terms in ε and μ, and equating the coefficients of like powers of ε i μ j , respectively, for i, j � 0, 1, . .…”

“…Many approximate methods have been improved, such as Graef and Kong [8], Hovhannisyan and Vulanovic [9], Bonfoh et al [10], Barbu and Cosma [11], Faye et al [12], Samusenko [13], Mo [14], Das et al [15,16], and so on [17][18][19][20][21][22][23][24][25][26]. By using the singular perturbation theories, Feng et al also studied a class of nonlinear singular perturbation problems [27][28][29][30][31][32][33][34].…”

“…and by using the multiple scales variable, the method of component expansion, and the singular perturbation theory, we proved the existence of solution to the problem and the uniformly valid asymptotic estimation. Feng et al [34] in 2018 considered a class of nonlinear differential-integral singular perturbation problem for the disturbed evolution equations. Using the singular perturbation method, the structure of solution to problem is discussed in the cases of two small parameters under suitable conditions.…”