Geodesic
Initial-boundary value problems for nonlinear pseudoparabolic equations in a critical case
Electronic Journal of Differential Equations, Tome 2007 (2007).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study nonlinear pseudoparabolic equations, on the half-line in a critical case, $$\displaylines{ \partial _{t}( u-u_{xx}) -\alpha u_{xx}=\lambda |u| u,\quad x\in \mathbb{R}^{+},\; t>0, \cr u( 0,x) =u_{0}( x) , \quad x\in \mathbb{R}^{+}, \cr u(t,0)=0, }$$ where $\alpha >0, \lambda \in \mathbb{R}$. The aim of this paper is to prove the existence of global solutions to the initial-boundary value problem and to find the main term of the asymptotic representation of solutions.
Classification : 35Q35
Keywords: dissipative nonlinear evolution equation, Sobolev equation, large time asymptotic behavior 
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     author = {Kaikina, Elena I.},
     title = {Initial-boundary value problems for nonlinear pseudoparabolic equations in a critical case},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a115/}
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Kaikina, Elena I. Initial-boundary value problems for nonlinear pseudoparabolic equations in a critical case. Electronic Journal of Differential Equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a115/