A quarter-plane problem for the modified Burgers’ equation

2013 ◽  
Vol 54 (9) ◽  
pp. 091502 ◽  
Author(s):  
J. A. Leach
Keyword(s):  
Plane Problem ◽  
Burgers Equation ◽  
Modified Burgers Equation ◽  
Quarter Plane

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

2019 ◽  
Vol 52 (1) ◽  
pp. 237-248
Author(s):  
Esen Hanaç
Keyword(s):  
Boundary Condition ◽  
Analytic Solution ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Condition ◽  
Quarter Plane ◽  
Initial Boundary Value ◽  
Good Agreement

AbstractIn this paper we investigate an initial-boundary value problem for the Burgers equation on the positive quarter-plane; $\matrix{ {{v_t} + v{v_x} - {v_{xx}} = 0,\,\,\,x > 0,\,\,\,t > 0,} \cr {v\left( {x,0} \right) = {u_ + },\,\,\,x > 0,} \cr {v\left( {0,t} \right) = {u_b},\,\,t > 0,} \cr }$ 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.

Time-dependent non-planar DIA shock waves in non-extensive dusty plasma

2013 ◽  
Vol 79 (5) ◽  
pp. 545-551 ◽  
Author(s):  
S. YASMIN ◽  
M. ASADUZZAMAN ◽  
A. A. MAMUN
Keyword(s):  
Shock Waves ◽  
Dusty Plasma ◽  
Burgers Equation ◽  
Spherical Geometry ◽  
Bounded Geometry ◽  
Modified Burgers Equation ◽  
Basic Features ◽  
Ion Acoustic Shock Waves ◽  
Stationary Dust ◽  
Dusty Plasma System

AbstractThe propagation of dust ion-acoustic shock waves (DIASHWs) in an unmagnetized dissipative dusty plasma system consisting of inertial ions, non-inertial, non-extensive q-distributed electrons, and negatively charged stationary dust is investigated in bounded non-planar (cylindrical and spherical) geometry. A modified Burgers equation is derived and its numerical solution is obtained. It is found that the basic features of DIASHWs are significantly modified by the effects of electron non-extensivity and ion kinematic viscosity in bounded geometry. It is also shown that the propagation characteristics of non-planar DIASHWs in a non-extensive plasma are qualitatively different from those of planar ones.

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