CEU Electronic Theses and Dissertations, 2015
| Author | Gonzalez de Cossio, Francisco Jose |
|---|---|
| Title | First-order Differential Inclusions Governed by Maximal Monotone Operators |
| Summary | We exhibit an existence and uniqueness result for a differential inclusion of first order, with initial condition, governed by a maximal monotone operator on a Hilbert space. In order to do this, we first expose the main proofs in maximal monotone theory needed for the existence and uniqueness theorem. We also present the concept of subdifferential of a convex function and show the proof of its maximal monotonicity under certain conditions. This theory helps to solve equations when there is a lack of linearity and continuity of the associated operators. The importance of this is then exhibited by three main applications: The Heat (Diffusion) Equation, the Dynamics of a Model for Wheeled Vehicles and the Nonlinear Wave Equation. The Nonlinear Wave Equation is solved assuming very mild conditions on the nonlinear term. |
| Supervisor | Morosanu, Gheorghe |
| Department | Mathematics MSc |
| Full text | https://www.etd.ceu.edu/2015/cossio_francisco.pdf |
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