Research
Research interests:
- Partial differential equations, especially
-
Phase field models (especially the Cahn-Hilliard equation) and their applications (e.g.,
tumor growth models)
-
Kinetic equations from plasma physics (e.g., Vlasov-Poisson and
Vlasov-Maxwell equations).
- Calculus of variations
- Optimal control
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Optimal control theory for problems with PDE constraints
-
Shape and topology optimization via phase-field approach
- Numerical methods and simulations for PDEs
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Finite element methods
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Particle-in-cell methods for kinetic equations
Research projects and collaborators:
Analysis and numerical methods for anisotropic diffuse interface models
with
Analysis and optimal control of magneto-viscoelastic fluids
with
Analysis and optimal control of phase-field models for tumor growth
with
Analysis of stratified water waves
with
Elliptic problems with bulk-surface coupling: Well-posedness, regularity theory, eigenvalue problems
with
Nonlocal-to-local convergence and its application to phase-field models
with
Optimal control and confinement of plasmas modeled by Vlasov equations
with
Shape and topology optimization via multi-phase-field approach
with
Two-phase flows with bulk-surface interaction
described by dynamic boundary conditions
with
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