Initial value problems for the Carleman equation

DOI10.1016/0362-546X(80)90059-0zbMath0431.35024OpenAlexW1998519107MaRDI QIDQ3868152

Hans G. Kaper, Gary K. Leaf

Publication date: 1980

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(80)90059-0

zbMATH Keywords

convergence ratesinitial value problemsnonlinear semigroupsCauchy problemsaccretive operatorskinetic theory of gasesnonexpansive semigroupperturbed problemCarleman equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear accretive operators, dissipative operators, etc. (47H06) Nonlinear differential equations in abstract spaces (34G20) Initial value problems for nonlinear first-order PDEs (35F25) Initial value problems for linear higher-order PDEs (35G10) Kinetic theory of gases in equilibrium statistical mechanics (82B40) Higher-order parabolic equations (35K25)

Related Items (11)

The carleman system with positive measures as initial data-generalized solutions ⋮ A general approach to solution of partial differential equation systems ⋮ Convergence to a traveling wave in the lgarithmic diffusion equation with a bistable nonlinearity ⋮ Spreading and Extinction of Solutions to the Logarithmic Diffusion Equation with a Logistic Reaction ⋮ Control of modeling errors in the coupling of linear transport and diffusion models ⋮ Diffusion approximation for a class of Markov processes satisfying a nonlinear Fokker-Planck equation ⋮ On a nonlinear singular diffusion problem:existence and uniqueness ⋮ Asymptotic behavior of solutions to the logarithmic diffusion equation with a linear source ⋮ On a nonlinear singular diffusion problem: convergence to a traveling wave ⋮ The fluid dynamical limit of the Carleman equation with reflecting boundary ⋮ Initial boundary value problems for the Carleman equation

Cites Work

• On the Broadwell model of the Boltzmann equation for a simple discrete velocity gas
• On the Carleman's model for the Boltzmann equation and its generalizations
• Sur la résolution exacte et approchee d'un problème hyperbolique non linéaire de T. Carleman
• Convergence of semigroups with an application to the carleman equation
• Convergence of Sequences of Semigroups of Nonlinear Operators with an Application to Gas Kinetics
• Norm Preserving Extensions of Linear Transformations on Hilbert Spaces
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