PhD Project: nonlinear and nonlocal partial differential equations

Complex systems in nature and in applied sciences are often described by nonlinear and nonlocal partial differential equations (PDEs). A typical example is the (spatial and/or time) fractional Fokker-Planck equation which arises in the study of complex physical systems involving anomalously slow diffusion [ACV16, HIK+18]. A mathematical analysis of such an equation is pivotal for the understanding and control of physical systems. However, it is often challenging due to the involved nonlinearity and nonlocality. Variational methods, in particular Wasserstein gradient flow structures [JKO98, Vil03] has been proven to be a powerful and versatile tool for the analysis of nonlinear and nonlocal PDEs.

The aim of this PhD project is to develop Wasserstein gradient flow-type formulations for nonlinear and nonlocal partial differential equations. The key challenge would be to build up new optimal transportation cost functionals and/or new approximation schemes.

The project will be based at the School of Mathematics at University of Birmingham and will be supervised by Dr. Hong Duong (possibly with another member staff). The School of Mathematics at the University of Birmingham is an internationally leading centre for mathematical research, with particular strengths in mathematical analysis, biological mathematics, combinatorics and optimization. The PhD candidate will have many opportunities to interact with leading scientists at the school of mathematics and other departments.

Recent collaborative works of Dr. Hong Duong in the direction of research of the project include [DLPS17, DT18, DLP+18, DL19, DJ19].

Applications before 31 January is strongly encouraged. Please contact [Email Address Removed] for any questions.