Cockburn, B.; Gripenberg, G.; Londen, S.-O. Continuous dependence on the nonlinearity of viscosity solutions of parabolic equations. (English) Zbl 0973.35107 J. Differ. Equations 170, No. 1, 180-187 (2001). The paper proposes an upper bound for \((u-v)\) where \(u\) is a viscosity subsolution of \( u_t+F(u,D_xu,D^2_{xx}u)=0 \) and \(v\) is a viscosity supersolution of \( v_t+G(v,D_xv,D^2_{xx}v)=0 \) in \((0,\infty)\times\Omega\) with Neumann boundary conditions and where \(\Omega\) is an open convex set. Reviewer: Dian K.Palagachev (Bari) Cited in 1 ReviewCited in 5 Documents MSC: 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs Keywords:fully nonlinear parabolic equations; viscosity supersolution; Neumann boundary condition; viscosity subsolution PDFBibTeX XMLCite \textit{B. Cockburn} et al., J. Differ. Equations 170, No. 1, 180--187 (2001; Zbl 0973.35107) Full Text: DOI Link References: [1] B. Cockburn, D. A. French, and, T. E. Peterson, A posteriori error estimates for general numerical methods for Hamilton-Jacobi equations, Math. Comp, to appear.; B. Cockburn, D. A. French, and, T. E. Peterson, A posteriori error estimates for general numerical methods for Hamilton-Jacobi equations, Math. Comp, to appear. · Zbl 1063.65093 [2] Cockburn, B.; Gripenberg, G., Continuous dependence on the nonlinearities of solutions of degenerate parabolic equations, J. Differential Equations, 151, 231-251 (1999) · Zbl 0921.35017 [3] Crandall, M. G.; Ishii, H.; Lions, P. L., User’s guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., 27, 1-67 (1992) · Zbl 0755.35015 [4] Crandall, M. G.; Lions, P. L., Two approximations of solutions of Hamilton-Jacobi equations, Math. Comp., 43, 1-19 (1984) · Zbl 0556.65076 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.