| 书目名称 | Dual Variational Approach to Nonlinear Diffusion Equations |
| 编辑 | Gabriela Marinoschi |
| 视频video | |
| 概述 | Presents technique for proving existence of solutions to nonlinear diffusion equations.Utilizes specific examples that can model real-world physical processes.Chapters develop methods for treating par |
| 丛书名称 | Progress in Nonlinear Differential Equations and Their Applications |
| 图书封面 |  |
| 描述 | .This monograph explores a dual variational formulation of solutions to nonlinear diffusion equations with general nonlinearities as null minimizers of appropriate energy functionals. The author demonstrates how this method can be utilized as a convenient tool for proving the existence of these solutions when others may fail, such as in cases of evolution equations with nonautonomous operators, with low regular data, or with singular diffusion coefficients. By reducing it to a minimization problem, the original problem is transformed into an optimal control problem with a linear state equation. This procedure simplifies the proof of the existence of minimizers and, in particular, the determination of the first-order conditions of optimality. The dual variational formulation is illustrated in the text with specific diffusion equations that have general nonlinearities provided by potentials having various stronger or weaker properties. These equations can represent mathematical modelsto various real-world physical processes. Inverse problems and optimal control problems are also considered, as this technique is useful in their treatment as well.. |
| 出版日期 | Book 2023 |
| 关键词 | Dual variational inequalities; Brezis-Ekeland principle; Legendre-Fenchel inequalities; Convex optimiza |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-031-24583-1 |
| isbn_softcover | 978-3-031-24585-5 |
| isbn_ebook | 978-3-031-24583-1Series ISSN 1421-1750 Series E-ISSN 2374-0280 |
| issn_series | 1421-1750 |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
发表于 2025-3-21 18:29:20
