Geodesic
Asymptotic estimate of solutions in a 4th-order parabolic equation with the Frobenius norm of a Hessian matrix
Canadian mathematical bulletin, Tome 68 (2025) no. 1, pp. 91-108

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DOI

This paper deals with a 4th-order parabolic equation involving the Frobenius norm of a Hessian matrix, subject to the Neumann boundary conditions. Some threshold results for blow-up or global or extinction solutions are obtained through classifying the initial energy and the Nehari energy. The bounds of blow-up time, decay estimates, and extinction rates are studied, respectively.
DOI : 10.4153/S0008439524000572
Mots-clés : 4th-order parabolic equation, Hessian matrix, global existence, blow-up time, extinction rate 
Li, Ke; Liu, Bingchen; Dou, Jiaxin. Asymptotic estimate of solutions in a 4th-order parabolic equation with the Frobenius norm of a Hessian matrix. Canadian mathematical bulletin, Tome 68 (2025) no. 1, pp. 91-108. doi: 10.4153/S0008439524000572
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     author = {Li, Ke and Liu, Bingchen and Dou, Jiaxin},
     title = {Asymptotic estimate of solutions in a 4th-order parabolic equation with the {Frobenius} norm of a {Hessian} matrix},
     journal = {Canadian mathematical bulletin},
     pages = {91--108},
     year = {2025},
     volume = {68},
     number = {1},
     doi = {10.4153/S0008439524000572},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000572/}
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