NONLINEAR EVOLUTION GOVERNED BY ACCRETIVE OPERATORS IN BANACH SPACES: ERROR CONTROL AND APPLICATIONS

DOI10.1142/S0218202506001224zbMath1098.65092OpenAlexW2045453641MaRDI QIDQ5470139

Giuseppe Savaré, Ricardo H. Nochetto

Publication date: 29 May 2006

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202506001224

zbMATH Keywords

Banach spacesconservation lawsHamilton-Jacobi equations\(m\)-accretive operatorsa posteriori error estimatesvariable stepsizecontraction semigroupsdegenerate parabolic equationsdissipative PDEabstract nonlinear evolution equationsEuler methods

Mathematics Subject Classification ID

Nonlinear accretive operators, dissipative operators, etc. (47H06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical solutions to equations with nonlinear operators (65J15) Nonlinear evolution equations (47J35)

Related Items (15)

Efficient Stability-Preserving Numerical Methods for Nonlinear Coercive Problems in Vector Space ⋮ A Posteriori Estimates for the Stochastic Total Variation Flow ⋮ Convergence of the variable two-step BDF time discretisation of nonlinear evolution problems governed by a monotone potential operator ⋮ Convergence order of implicit Euler numerical scheme for maximal monotone differential inclusions ⋮ Hölder regularity for abstract semi-linear fractional differential equations in Banach spaces ⋮ Continuum limit of p-Laplacian evolution problems on graphs: L^q graphons and sparse graphs ⋮ Asymptotic uniform boundedness of energy solutions to the Penrose-Fife model ⋮ Nonlinear semigroups for nonlocal conservation laws ⋮ Dissipative probability vector fields and generation of evolution semigroups in Wasserstein spaces ⋮ Stability and Convergence of Stepsize-Dependent Linear Multistep Methods for Nonlinear Dissipative Evolution Equations in Banach Space ⋮ A posteriori error analysis for higher order dissipative methods for evolution problems ⋮ A posteriori error estimates and maximal regularity for approximations of fully nonlinear parabolic problems in Banach spaces ⋮ Stiffly accurate Runge–Kutta methods for nonlinear evolution problems governed by a monotone operator ⋮ Asymptotic almost-equivalence of Lipschitz evolution systems in Banach spaces ⋮ Variable time-step \(\vartheta\)-scheme for nonlinear evolution equations governed by a monotone operator

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Difference approximation of Cauchy problems for quasi-dissipative operators and generation of nonlinear semigroups
• On the relation of the operator \(\partial/\partial s+partial/\tau\) to evolution governed by accretive operators
• Continuous dependence on the nonlinearities of solutions of degenerate parabolic equations
• Semi-linear second-order elliptic equations in \(L^1\)
• The semigroup approach to first order quasilinear equations in several space variables
• Some Relations Between Nonexpansive and Order Preserving Mappings
• User’s guide to viscosity solutions of second order partial differential equations
• Error control of nonlinear evolution equations
• A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations
• Error Analysis for Implicit Approximations to Solutions to Cauchy Problems
• Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces

This page was built for publication: NONLINEAR EVOLUTION GOVERNED BY ACCRETIVE OPERATORS IN BANACH SPACES: ERROR CONTROL AND APPLICATIONS