The Method of Characteristics and Classical Solutions of First Order Pdes
| dc.contributor.advisor | Abdi Tadesse (PhD) | |
| dc.contributor.author | Abiy Surafel | |
| dc.date.accessioned | 2020-12-14T10:34:55Z | |
| dc.date.accessioned | 2023-11-04T12:31:04Z | |
| dc.date.available | 2020-12-14T10:34:55Z | |
| dc.date.available | 2023-11-04T12:31:04Z | |
| dc.date.issued | 2014-08-08 | |
| dc.description.abstract | The Method of Characteristics is a Powerful Method that Allows one to reduce any Rst-order linear PDE to an ODE, Which Can be Subsequently Solved Using ODE techniques and it can be generalized to quasilinear equations as well. the principal results of this paper are: 1) The Cauchy problem @u @t + f(t; x; u; @u @x ) = 0; inft > 0; x 2 Rng; u(0; x) = (x); onft = 0; x 2 Rng has locally a unique C2-solution. 2) If the Jacobian (Dx=Dy)(t; y) of the mapping x = x(t; y) vanishes some- where, it is impossible to extend the C2-solution beyond a point where the Jacobian vanishes. 3) Suppose that the characteristic curves do not meet in a neighborhood of the point where the Jacobian vanishes. Then the solution keeps being of class C1, but not of class C2, in the neighborhood of the point. | en_US |
| dc.identifier.uri | http://etd.aau.edu.et/handle/123456789/24036 | |
| dc.language.iso | en | en_US |
| dc.publisher | Addis Ababa University | en_US |
| dc.subject | Method | en_US |
| dc.subject | Characteristics | en_US |
| dc.subject | Classical Solutions | en_US |
| dc.subject | Order Pdes | en_US |
| dc.title | The Method of Characteristics and Classical Solutions of First Order Pdes | en_US |
| dc.type | Thesis | en_US |