On the evolution of solutions of Burgers equation on the positive quarter-plane
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,$\matrix{ {{v_t} + v{v_x} - {v_{xx}} = 0,\,\,\,x > 0,\,\,\,t > 0,} \cr {v\left( {x,0} \right) = {u_ +...
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| Format: | Article |
| Language: | English |
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De Gruyter
2019-06-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | https://doi.org/10.1515/dema-2019-0020 |
| _version_ | 1818741165074153472 |
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| author | Hanaç Esen |
| author_facet | Hanaç Esen |
| author_sort | Hanaç Esen |
| collection | DOAJ |
| description | In this paper we investigate an initial-boundary value problem for the Burgers equation on the positive quarter-plane; vt+vvx-vxx=0, x>0, t>0,v(x,0)=u+, x>0,v(0,t)=ub, t>0,$\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. |
| first_indexed | 2024-12-18T01:52:17Z |
| format | Article |
| id | doaj.art-708d9369d63348c990a984fb67fe43a4 |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-12-18T01:52:17Z |
| publishDate | 2019-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-708d9369d63348c990a984fb67fe43a42022-12-21T21:24:59ZengDe GruyterDemonstratio Mathematica2391-46612019-06-0152123724810.1515/dema-2019-0020dema-2019-0020On the evolution of solutions of Burgers equation on the positive quarter-planeHanaç Esen0Department of Mathematics, Adiyaman University, TurkeyIn 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.https://doi.org/10.1515/dema-2019-0020burgers equationtraveling wave solution (tw)numeric solutions65mxx |
| spellingShingle | Hanaç Esen On the evolution of solutions of Burgers equation on the positive quarter-plane Demonstratio Mathematica burgers equation traveling wave solution (tw) numeric solutions 65mxx |
| title | On the evolution of solutions of Burgers equation on the positive quarter-plane |
| title_full | On the evolution of solutions of Burgers equation on the positive quarter-plane |
| title_fullStr | On the evolution of solutions of Burgers equation on the positive quarter-plane |
| title_full_unstemmed | On the evolution of solutions of Burgers equation on the positive quarter-plane |
| title_short | On the evolution of solutions of Burgers equation on the positive quarter-plane |
| title_sort | on the evolution of solutions of burgers equation on the positive quarter plane |
| topic | burgers equation traveling wave solution (tw) numeric solutions 65mxx |
| url | https://doi.org/10.1515/dema-2019-0020 |
| work_keys_str_mv | AT hanacesen ontheevolutionofsolutionsofburgersequationonthepositivequarterplane |