On solvability of the first initial-boundary value problem for quasilinear pseudoparabolic equations

• Published in: Applied mathematics and computation Vol. 246; pp. 112 - 120
• Main Author: Amirov, Sherif
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.11.2014
• Subjects: 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; Composite type equations; Quasilinear pseudoparabolic equations; Non-linear equations; Boundary value problem; Equations of Sobolev type
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2014.07.095

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.