セミナーの予定

2025年10月9日(木) 16:30-18:00

会場

東北大学 合同A棟8階801室

発表者

Luca Scarpa 氏 ( Politecnico di Milano )

題目

The effect of noise on doubly nonlinear evolution equations

要旨

We give an overview of some recent results for doubly nonlinear stochastic evolution equations in Hilbert spaces. In the first part of the talk we introduce the prototypes of the problems in consideration and we discuss the main existence results. Secondly, we focus on the direction of uniqueness by noise for doubly nonlinear evolutions by means of the associated Kolmogorov equations, highlighting some recent contributions and open problems. The works presented in the talk are based on joint collaborations with Prof. Ulisse Stefanelli (University of Vienna, Austria) and Prof. Carlo Orrieri (University of Pavia, Italy).

2025年10月16日(木) 16:30-18:00

会場

東北大学 合同A棟8階801室

発表者

Philippe Souplet 氏 ( Université Sorbonne Paris Nord )

題目

Diffusive Hamilton-Jacobi equations: gradient blow-up singularities, Liouville-type theorems and continuation after blow-up

要旨

We consider the diffusive Hamilton-Jacobi equation $u_t-\Delta u=|\nabla u|^p$ with homogeneous Dirichlet boundary conditions, which plays an important role in stochastic optimal control theory and in certain models of surface growth (KPZ). Despite its simplicity, it displays a variety of interesting and surprising behaviors and significant progress has been made in the past ten years. We will discuss the following issues:
- Gradient blow-up (GBU) on the boundary: time rate, single-point GBU, space and time-space profiles;
- Liouville type theorems and their applications;
- Continuation after GBU as a global viscosity solution with loss and recovery of boundary conditions.