Electron. J. Differential Equations, Vol. 2021 (2021), No. 73, pp. 1-9.

Decay estimates for solutions of evolutionary damped p-Laplace equations

Farid Bozorgnia, Peter Lewintan

In this note, we study the asymptotic behavior, as t tends to infinity, of the solution u to the evolutionary damped p-Laplace equation

with Dirichlet boundary conditions. Let u* denote the stationary solution with same boundary values, then we prove the W1,p-norm of u(t) - u* decays for large t like t-1/((p-1)p), in the degenerate case p>2.

Submitted July 8, 2021. Published September 10, 2021.
Math Subject Classifications: 35B40, 35L70.
Key Words: p-Laplace; telegraph equation; asymptotic behavior; convexity.
DOI: https://doi.org/10.58997/ejde.2021.73

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Farid Bozorgnia
CAMGSD, Instituto Superior Técnico
University of Lisbon
Av. Rovisco Pais
1049-001 Lisbon, Portugal
email: farid.bozorgnia@tecnico.ulisboa.pt
Peter Lewintan
Faculty of Mathematics
University of Duisburg-Essen
Thea-Leymann-Str. 9, 45127 Essen, Germany
email: peter.lewintan@uni-due.de

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