Nonlinear Partial Differential Equations

By Friedrich Sauvigny. 2012

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Reduced basis approximation and a posteriori error bounds for 4D-Var data assimilation (2018, background): “A preliminary improvement of the model itself before estimating the state can result in an improved state estimate, see e.g. the application in Habert et al. (2016).”
Porous media equations with two weights: smoothing and decay properties of energy solutions via Poincar\'e inequalities (2012, background): “For a thorough analysis of smoothing and decay properties of solutions to large classes of nonlinear evolution equations on RN , see the monograph [52] (see also [26]).”
$ L^p $-$ L^q $ estimates for the damped wave equation and the critical exponent for the nonlinear problem with slowly decaying data (2017, background): “Namely, G(t)g is the solution of (4) with v(0) = g (see [7]).”