Comparison theorems for nonlinear evolution equations and their application to the investigation of the dependence of the solutions of the equation \(u_ t=\Delta \phi (u)\) on \(\phi\) and on the boundary conditions

DOI10.1007/BF01104876zbMath0643.35011OpenAlexW2074842351MaRDI QIDQ1101880

M. I. Khazan

Publication date: 1984

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01104876

zbMATH Keywords

generalized solutionsestimatescomparison theoremsdissipative operatorsCauchyDirichletdependence of the solutions

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Nonlinear differential equations in abstract spaces (34G20) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Cites Work

• Difference approximation of Cauchy problems for quasi-dissipative operators and generation of nonlinear semigroups
• On the nonlinear semi-groups associated with \(u_t=\Delta \beta (u)\) and \(\varphi(u_t)=\Delta u\)
• Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces
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