On solvability of the first initial-boundary value problem for quasilinear pseudoparabolic equations
In the paper, the solvability of the first initial-boundary value problem for a quasilinear pseudoparabolic equationut-Δut-∂∂xibijx,t,uuxj+cix,t,uuxi+ϑx,t,u=fx,twith increasing with respect to ζ functions bijx,t,ζ,cix,t,ζ and ϑx,t,ζ was investigated. The existence and uniqueness of regular solutions...
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| Published in | Applied mathematics and computation Vol. 246; pp. 112 - 120 |
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| Format | Journal Article |
| Language | English |
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Elsevier Inc
01.11.2014
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| ISSN | 0096-3003 1873-5649 |
| DOI | 10.1016/j.amc.2014.07.095 |
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| Abstract | In the paper, the solvability of the first initial-boundary value problem for a quasilinear pseudoparabolic equationut-Δut-∂∂xibijx,t,uuxj+cix,t,uuxi+ϑx,t,u=fx,twith increasing with respect to ζ functions bijx,t,ζ,cix,t,ζ and ϑx,t,ζ was investigated. The existence and uniqueness of regular solutions are proven. |
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| AbstractList | In the paper, the solvability of the first initial-boundary value problem for a quasilinear pseudoparabolic equation ut- Delta ut- partial differential partial differential xibijx,t,uuxj+cix,t,uuxi+[thetav]x,t,u= fx,t with increasing with respect to zeta zeta functions bijx,t, zeta ,cix,t, zeta and [thetav](x,t, zeta )[thetav]x,t, zeta was investigated. The existence and uniqueness of regular solutions are proven. In the paper, the solvability of the first initial-boundary value problem for a quasilinear pseudoparabolic equationut-Δut-∂∂xibijx,t,uuxj+cix,t,uuxi+ϑx,t,u=fx,twith increasing with respect to ζ functions bijx,t,ζ,cix,t,ζ and ϑx,t,ζ was investigated. The existence and uniqueness of regular solutions are proven. |
| Author | Amirov, Sherif |
| Author_xml | – sequence: 1 givenname: Sherif surname: Amirov fullname: Amirov, Sherif email: samirov@karabuk.edu.tr organization: Department of Mathematics, Faculty of Sciences, Karabuk University, 78050 Karabuk, Turkey |
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| Cites_doi | 10.1002/num.20325 10.1137/0501001 10.1016/j.apnum.2004.02.002 10.1002/num.20071 10.1002/num.20019 10.1016/j.chaos.2005.11.010 10.1137/0524082 10.1016/j.apm.2008.03.006 |
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| SubjectTerms | Boundary value problem Boundary value problems Composite type equations Computation Equations of Sobolev type Initial value problems Mathematical analysis Mathematical models Non-linear equations Quasilinear pseudoparabolic equations Uniqueness |
| Title | On solvability of the first initial-boundary value problem for quasilinear pseudoparabolic equations |
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