I classify myself as a **theoretical applied mathematician** - a person that studies problems arising from applied sciences (like biological growth and fluid flow) and aims for theoretical results.

My work mainly involves proving mathematical theorems about various models used in applied sciences. These are statements regarding certain properties of solutions to partial differential equations that would be useful for scientists.

Below you can find a brief summary of my research interests and the research projects I am responsible as principal investigator.## Research Interests

## Research projects (as Principal Investigator)

### Hong Kong RGC General Research Fund

My work mainly involves proving mathematical theorems about various models used in applied sciences. These are statements regarding certain properties of solutions to partial differential equations that would be useful for scientists.

Below you can find a brief summary of my research interests and the research projects I am responsible as principal investigator.

**Mathematical Modelling**

Derive mathematical models for multi-component materials and fluids with applications in biological sciences and industry, such as tumour growth and soluble surfactants in two-phase flows.**Analysis**

Mathematical analysis of coupled systems of elliptic and parabolic partial differential equations, sometimes with degenerate and singular terms. Establishing important properties such as existence and uniqueness of solutions, and various interesting asymptotic limits.**Optimal Control**

Employ optimal control methodology and Tikhonov regularisation to solve inverse identification problems inferring model parameters from data, and geometric inverse problems identifying location of interfaces between two different materials. Investigate convergence to solutions of the original inverse problem as the Tikhonov parameter tends to zero.**Numerical schemes**

Develop energy stable numerical schemes for the simulation of nonlinear partial differential equations with bulk-surface interactions and dynamic boundary conditions. Establish existence and convergence of discrete solutions.

**Optimising the design of support structures in additive manufacturing with phase fields**

[RGC project number (12300321)] Period: 01/01/2022 to 31/12/2024. Funding: $391,015 HKD**Modelling and analysis of diffuse interface models for two-phase micropolar fluid flows**

[RGC project number (14303420)] Period: 01/01/2021 to 31/12/2023. Funding: $555,754 HKD**On Cahn-Hilliard models with singular potentials and source terms**

[RGC project number (14302319)] Period: 01/09/2019 to 31/08/2022. Funding: $502,444 HKD**Mathematical studies of a phase field approach to shape optimization**

[RGC project number (14302218)] Period: 01/01/2019 to 31/12/2021. Funding: $456,452 HKD