Fábio L. Oliveira, Diego G. Santos, Maria J. M. Silva, Dennys J. C. Silva
Published 2025-05-09Version 1
In this paper, we introduce a logarithmic-type second-order model with a non-local logarithmic damping mechanism in $R^N$. We present a motivation with a spectral approach to consider the equation, we consider the Cauchy problem associated with the model. More precisely, we study the asymptotic behavior of solutions as $t$ goes to infinity in $L^2$-sense; namely, we prove results on the asymptotic profile and optimal decay of solutions as time goes to infinity in $L^2$-sense.
Second order $L_p$ estimates for subsolutions of fully nonlinear equations
Non-divergence Parabolic Equations of Second Order with Critical Drift in Lebesgue Spaces
Second Order $L^\infty$ Variational Problems and the $\infty$-Polylaplacian
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