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Nonlinear Parabolic Equations, Favard Classes, and Regularity
| Content Provider | Scilit |
|---|---|
| Author | Goldstein, Gisèle Ruiz |
| Copyright Year | 2020 |
| Description | This chapter discusses the role of a m-dissipative operator (not necessarily linear) on a Banach space. It utilizes the Crandall-Liggett theorem so as to determine a contraction semigroup. The Favard class (or the generalized domain) is defined for solving the nonlinear parabolic equations. The Favard class is an invariant set for the semigroup. Hence, the Favard class contains information on spatial regularity of a problem. The chapter calculates the Favard class explicitly in the case of a nonlinear parabolic problem with degeneracy and draws some conclusions about regularity. The problem of calculating the Favard class for the nonlinear parabolic problem is discussed with either Dirichlet or nonlinear boundary conditions. The chapter considers a more general operator with several different types of boundary conditions, so that even in the case where no lower order terms are present, new results are provided. Book Name: stochastic processes and functional analysis |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2009-0-11244-9&isbn=9781003067597&doi=10.1201/9781003067597-22&format=pdf |
| Ending Page | 263 |
| Page Count | 11 |
| Starting Page | 253 |
| DOI | 10.1201/9781003067597-22 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2020-09-23 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Stochastic Processes and Functional Analysis Mathematical Physics Boundary Semigroup Equations Chapter Nonlinear Parabolic Favard Class |
| Content Type | Text |
| Resource Type | Chapter |
