Non-linear elliptic and parabolic equations and systems appearing in geometry, physics and engineering: e.g. the minimum surface equation, the equation of Monge-Ampere, the equation of anisotopic diffusion in the theory image clarification, viscose solutions, diffraction problems of equations with non-continuous coefficients and others.
Nonlinear equations, Integrable systems, Differential geometry, Symmetry and singularity theory, Geometric methods in Physics.
The research interests of Dr. Boyadzhiev include: the comparison principle for systems of elliptic and parabolic differential equations; PDEs, including both cooperative, and non-cooperative systems; movement of waves in a solid body - in particular, the use of characteristics to track the path of seismic waves from an earthquake source to reception stations; development of methods for choosing the optimal solution of nonlinear vapor problem in mathematical modelling of Earth structure; deterministic models in geophysics and financial markets.
