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Research Interests

AREAS OF SPECIALIZATION:

  • Differential Equations and Partial Differential Inequalities
  • Nonlinear Analysis
  • Mathematical Biology, Ecology
  • Fluid dynamics

My main interests lie in mathematical biology, boundary value problems and boundary layer problems.

Predator-prey systems: The dynamical relationship between predators and their prey, which is one of important themes in ecology, can be modeled by establishing predator prey systems of two first-order differential equations with suitable functional responses. The qualitative theories of dynamical systems are used and the dynamical behaviours of such predator-prey systems with initial states near equilibria can be predicted for appropriate ranges of parameters involved. These dynamical behaviours not only provide predication whether the two species will suffer from mutual extinction but also get insight into the optimal management of renewable resources like fishery and forestry.

Boundary value problems: Many problems arising from nonlinear mechanics, engineering, physics and biology can be changed into suitable ordinary, fractional, and partial differential equations with various boundary conditions. In most of these problems, the physical interest lies in the existence and uniqueness of positive solutions of these equations. The main interest is to establish new theories or apply the well-known theories from nonlinear analysis to treat the existence of one or multiple solutions.

In addition, reaction-diffusion equations arising from biology, Falkner-Skan equations arising from boundary layer problems, and variational inequalities and complementarity problems with applications to partial differential inequalities are also under investigation

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