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صفحة جديدة 1
“Nonlinear Analysis and Applied Mathematics” is a diverse group in nature and consists of excellent researchers in the field of nonlinear analysis as well as various disciplines of applied mathematics. The mathematical modeling of real world phenomena generally gives rise to nonlinear initial and boundary value problems. In order to solve the nonlinear problems, methods of nonlinear analysis play a crucial and pivotal role. The nonlinear analysts in our group are quite capable and competent to develop the new tools of nonlinear analysis and explain their usage in real world applications. The members of the group working in the field of differential equations will explore the existence, uniqueness and the methods of constructing the solutions for various kinds of differential equations occurring in the mathematical modeling of numerous physical problems. The researchers of the group working in the field of applied mathematics will make use of the techniques developed by their group fellows to solve the industry related problems. One objective of constituting this research group is to provide a platform for collaboration with one another as well as an opportunity to develop the linkage with the industry by getting involved in the research projects of optimum utility in the public sector. Another important objective is to promote and enhance the research activities in the university, and lend a helping hand to the research fellows working in different engineering and science departments by providing them the details of recently developed mathematical tools to solve the real world problems. Consequently, there is a strong possibility that a multidisciplinary research group may evolve later on. Other objectives include:
· To establish a research group in the field of differential equations, fixed point theory and applied mathematics.
· To develop new mathematical techniques for solving applied sciences problems.
· To produce application oriented research work of high quality.
· To create a friendly and cordial research environment in the department.
· To motivate the research fellows and graduate students in the department, which will definitely raise the standards of teaching and research of the department.
· To develop international research collaborations.
Importance of the Research Group to the University and the Society
The work of the proposed research group covers a variety of important fields such as fixed point theory and applications, optimization, analytic approximation of the solutions of nonlinear problems associated with the real world problems, stability theory of differential and integro-differential systems, investigation of fractional differential equations with the sphere of study ranging from the theoretical aspects of existence and uniqueness of solutions to the analytic and numerical methods for finding solutions, noise reduction problems, structural stability, vibration, plated structures and shells, nonlinear wave phenomena, wavelets, solitons and compactons, N-solitons, and singular perturbation in the diffusion process. These research fields have a great potential in the industry and highly useful to provide the descent solution to the practical problems arising in various phenomena of transport theory, the transfer of neutrons through thin plates and membranes in nuclear reactors, in the propagation of radiation through the atmosphere of planets and stars, and in several other transport problems, nonlinear optics, unsteady aerodynamics and aero elastic phenomena, biophysics, blood flow phenomena, visco-elasticity, visco-elastic panel in supersonic gas flow, fluid dynamics, electro dynamics of complex medium, many models of population growth, polymer rheology, neural network modeling, sandwich system identification, materials with fading memory, mathematical modeling of the diffusion of discrete particles in a turbulent fluid, heat conduction in materials with memory, theory of lossless transmission lines, theory of population dynamics, compartmental systems, nuclear reactors and mathematical modeling of a hereditary phenomena. In view of the above mentioned extensive applications, the proposed research group will have a great impact in the research activities of the university. As it reflects from the utility of the work, this research group has the potential to interact with the chemical, mechanical and electronics industries of the Kingdom and carries out joint research. In consequence, it will have a great impact on the economy of the Kingdom. Moreover, the present research group may also interact with the scientists of other universities in the Kingdom and create a larger research group of wider national interest.
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