On the evolution of solutions of Burgers equation on the positive quarter-plane

[摘要] In this paper we investigate an initial-boundary value problem for the Burgers equation on the positive quarter-plane; vt+vvx-vxx=0,   x>0,   t>0,v(x,0)=u+,   x>0,v(0,t)=ub,  t>0,$\matrix{ {{v_t} + v{v_x} - {v_{xx}} = 0,\,\,\,x > 0,\,\,\,t > 0,} \cr {v\left( {x,0} \right) = {u_ + },\,\,\,x > 0,} \cr {v\left( {0,t} \right) = {u_b},\,\,t > 0,} \cr }$ where x and t represent distance and time, respectively, and u + is an initial condition, ub is a boundary condition which are constants ( u + ≠ ub ). Analytic solution of above problem is solved depending on parameters ( u + and ub ) then compared with numerical solutions to show there is a good agreement with each solutions.

[学科分类] 外科医学

[关键词] Burgers equation;traveling wave solution (TW);numeric solutions