Blow-up phenomena and lifespan for a quasi-linear pseudo-parabolic equation at arbitrary initial energy level
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DOI: 10.1186/s13661-018-1079-7
Abstract: AbstractIn this paper, we continue to study the initial boundary value problem of the quasi-linear pseudo-parabolic equation ut−△ut−△u−div(|∇u|2q∇u)=up$$ u_{t}-\triangle u_{t}-\triangle u-\operatorname{div}\bigl(| \nabla u|^{2q}\nabla u\bigr)=u^{p} $$ which was studied by Peng et al. (Appl. Math. Lett.… read more here.
Keywords: parabolic equation; pseudo parabolic; energy; linear pseudo ... See more keywords
The Asymptotic Behavior and Blow-Up Rate of a Solution with a Lower Bound on the Highest Existence Duration for Semi-Linear Pseudo-Parabolic Equations
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DOI: 10.3390/math12193055
Abstract: This note addresses the initial-boundary value problem for a class of semi-linear pseudo-parabolic equations defined on a smooth bounded domain, with an emphasis on determining the asymptotic behavior and blow-up rate of the solution. Our… read more here.
Keywords: semi linear; pseudo parabolic; linear pseudo; behavior blow ... See more keywords