Geodesic
Initial-boundary value problems for nonlinear pseudoparabolic equations in a critical case
Electronic journal of differential equations, Tome 2007 (2007)
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 
@article{EJDE_2007__2007__a115,
     author = {Kaikina,  Elena I.},
     title = {Initial-boundary value problems for nonlinear pseudoparabolic equations in a critical case},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1133.35425},
     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/