### Ramesh Karki

Assistant Professor of Mathematics

Whitewater Hall 200D

765-973-8251

rkarki@iue.edu

#### Education

- PhD in Mathematics, 2015, University of Toledo
- M. A. in Mathematics, 2010, University of Toledo

#### Current Research Interests

- Partial Differential Equations (including Pseudo-differential Equations)
- Dynamical Systems
- Scholarship in Teaching and Learning

#### Peer Reviewed Publications

- R. Aceska, A. Arsie, R. Karki,
*On near-optimal time sampling for initial data best approximation, *Le Matematiche (Catania) 74 (2019), Number 1, 173-190, May 2019
- R. Karki,
*Sobolev Gradients & Application to Nonlinear Pseudo-differential Equations, *Neural, Parallel & Scientific Computations, Vol 22 (2014), Number 3, 359-373, September 2014

#### Submitted manuscripts

- R. Karki,
*On Approximating Initial Data in Some Linear Evolution Equations Involving Fractional Laplacian*, Analysis and Applications, December 2019
- R. Karki, Y. You,
*Fractional Order Semilinear Equations Using Variational Method, *Mathematics in Applied Sciences and Applications, December 2019

#### Selected Presentations

- R. Karki,
*Solutions to Fractional Order Semi-linear Equations Using Variational Method, *International Conference on Applications of Mathematics to Nonlinear Sciences, 2019 Pokhara, Nepal
- R. Karki,
*A finite sampling method for approximating initial data in some evolutionary equations, *The Ninth Ohio River Analysis Meetings 2019, University of Cincinnati
- R. Karki,
*A finite sampling method for approximating initial data in some evolutionary equations, *Joint Mathematics Meeting 2019, Baltimore
- R. Karki,
*Optimal approximation of initial data in some evolutionary PDEs via finite discrete sampling, *Joint Mathematics Meetings 2019, San Diego
- R. Karki,
*Approximation of solutions of non-linear* *PDEs from finitely many samples, *AMS Spring Central Meeting 2017, Indiana University Bloomington
- R. Karki,
*A Variational Type Method for Solving Nonlinear Pseudo-differential Equations, *Fall 2015 Meeting of Indiana Section of MAA, Purdue University North Central
- R. Karki,
*The Sobolev Gradients and Applications to Pseudo-differential Equations, *Joint Mathematics Meetings 2015, San Antonio
- R. Karki,
*The L*^{2}-gradient & Applications to Nonlinear Pseudo-differential Equations, Fall 2014 Meeting of Indiana Section of MAA, Trine University