Uniform in Time Description for Weak Solutions of the Hopf Equation with Nonconvex Nonlinearity
We consider the Riemann problem for the Hopf equation with concave-convex flux functions. Applying the weak asymptotics method we construct a uniform in time description for the Cauchy data evolution and show that the use of this method implies automatically the appearance of the Oleinik E-condition...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/101647 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832556144041656320 |
|---|---|
| author | Antonio Olivas Martinez Georgy A. Omel'yanov |
| author_facet | Antonio Olivas Martinez Georgy A. Omel'yanov |
| author_sort | Antonio Olivas Martinez |
| collection | DOAJ |
| description | We consider the Riemann problem for the Hopf equation with concave-convex flux functions. Applying the weak asymptotics method we construct a uniform in time description for the Cauchy data evolution and show that the use of this method implies automatically the appearance of the Oleinik E-condition. |
| format | Article |
| id | doaj-art-8de53f0e770d435f839a69926bef2f99 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8de53f0e770d435f839a69926bef2f992025-02-03T05:46:15ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/101647101647Uniform in Time Description for Weak Solutions of the Hopf Equation with Nonconvex NonlinearityAntonio Olivas Martinez0Georgy A. Omel'yanov1Departamento de Matematicas, Universidad de Sonora, Calle Rosales y Blvd Luis Encinas, s/n, 83000, Hermosillo, Sonora, MexicoDepartamento de Matematicas, Universidad de Sonora, Calle Rosales y Blvd Luis Encinas, s/n, 83000, Hermosillo, Sonora, MexicoWe consider the Riemann problem for the Hopf equation with concave-convex flux functions. Applying the weak asymptotics method we construct a uniform in time description for the Cauchy data evolution and show that the use of this method implies automatically the appearance of the Oleinik E-condition.http://dx.doi.org/10.1155/2009/101647 |
| spellingShingle | Antonio Olivas Martinez Georgy A. Omel'yanov Uniform in Time Description for Weak Solutions of the Hopf Equation with Nonconvex Nonlinearity International Journal of Mathematics and Mathematical Sciences |
| title | Uniform in Time Description for Weak Solutions of the Hopf Equation with Nonconvex Nonlinearity |
| title_full | Uniform in Time Description for Weak Solutions of the Hopf Equation with Nonconvex Nonlinearity |
| title_fullStr | Uniform in Time Description for Weak Solutions of the Hopf Equation with Nonconvex Nonlinearity |
| title_full_unstemmed | Uniform in Time Description for Weak Solutions of the Hopf Equation with Nonconvex Nonlinearity |
| title_short | Uniform in Time Description for Weak Solutions of the Hopf Equation with Nonconvex Nonlinearity |
| title_sort | uniform in time description for weak solutions of the hopf equation with nonconvex nonlinearity |
| url | http://dx.doi.org/10.1155/2009/101647 |
| work_keys_str_mv | AT antonioolivasmartinez uniformintimedescriptionforweaksolutionsofthehopfequationwithnonconvexnonlinearity AT georgyaomelyanov uniformintimedescriptionforweaksolutionsofthehopfequationwithnonconvexnonlinearity |