Asymptotic behavior of the shock solution for a class of nonlinear equations*

A Class of Nonlinear Singularly Perturbed Problems for Reaction Diffusion Equations with Boundary Perturbation

“…Recently, many scholars such as O'Malley, Jr. [18] , Adams, King and Tew [1] , Bell and Deng [2] Butuzov, Nefedov and Schneider [3] , Hamouda [5] , Kelley [6] , have done a great deal of work. Using the method of differential inequalities and others Mo et al considered also a class of singularly perturbed nonlinear boundary value problems [7][8][9][10][11][12][13][14][15][16][17]. In this paper using a special and simple method, we study a class of singularly perturbed nonlinear reaction diffusion problem with boundary perturbation.…”

Singularly perturbed solution to semilinear reaction diffusion equations with two parameters

“…Recently, many scholars, such as Ni and Wei [2] , Zhang [3] , Khasminskii and Yin [4] , Marques [5] , and Bobkova [6] , have done a great deal of work. Using the differential inequalities and other methods, Mo et al considered the singularly perturbed nonlinear boundary value problems for the ordinary differential equations [7] , the reaction diffusion equations [8][9][10] , the boundary value problems of the elliptic equations [11] , the ecological problems [12] , the shock layer solution of the nonlinear equations for the singularly perturbed problems [13][14] , and the problems of atmospheric physics [15][16][17][18] . In this paper, using a special singularly perturbed method, we study a class of initial boundary value problems for the reaction equations with two parameters.…”

A class of singular perturbation solutions to semilinear equations of fourth order

“…Recently, many scholars have done a great deal of work [1][2][3][4][5] . Using the method of differential inequalities and other methods, Mo et al considered a class of nonlinear singularly perturbed boundary value problems for the ordinary differential equations [6] , the reaction diffusion equations [7][8] , a class of activator inhibitor systems [9] , the ecological environment [10] , the shock wave [11] , the soliton [12][13] , the laser pulse [14] , the ocean science [15] , and the problems of atmospheric physics [16] . In this paper, using the method of lower and upper solutions and a special and simple singularly perturbed theory, we study a class of semilinear boundary value problems with two parameters.…”