Department of Differential Equations and Mathematical 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.

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.

Representations of Lie and Hecke algebras; Group algebras and differential and difference equations associated with quantum mechanics and mathematical physics.

Partial differential equations, Microlocal analysis, Spectral theory, Scattering theory, Dynamical systems.

The main research interests and publications of Peter Popivanov are in partial differential equations - linear and nonlinear micro-local analysis nonelliptic border problems and global solvability, hipoellipticity, propagation of singularities of weakly nonlinear hyperbolic equations and systems and applications in mechanics and geometry.

Partial differential equations and applications: Solvability and hypoellipticity for pseudodifferential operators with multiply characteristics; Scattering theory for hyperbolic equations and systems for moving obstacles; Nonlinear degenerate parabolic equations; BIEM for systems of elasticity in the domains with cracks.

Discrete Mathematics, Programming languages, parallel and distributed computing, cloud computing, information aggregation and retrieval.

I am working in the theory of differential equations, more precisely in partial differential equations (PDE), CNN modeling of complex nonlinear partial differential equations arising from applications in mathematical physics, in biology, in ecology, in mechanics etc.

Nonlinear dynamical systems related to infinite dimensional Lie algebras.

Research interests: Methods for Numerical Solving Nonlinear, Eigenvalue Boundary Problems, and Initial Problems, spectral and pseudospectral methods for wave and dispersion equations and dynamical systems

Hamiltonian PDEs and ODEs, dynamical systems, Riemannian and symplectic geometry, billiards.

Nonlinear equations, Integrable systems, Differential geometry, Symmetry and singularity theory, Geometric methods in Physics.

Theoretical and mathematical physics, Physics of space-time and gravity, Astrophysics and cosmology, Differential geometry and topology, Non-linear private differential equations, Numerical methods and computational physics