EPSRC Reference: 
EP/K024566/1 
Title: 
Monotonicity formula methods for nonlinear PDEs 
Principal Investigator: 
Karakhanyan, Dr A 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Sch of Mathematics 
Organisation: 
University of Edinburgh 
Scheme: 
First Grant  Revised 2009 
Starts: 
01 November 2013 
Ends: 
31 October 2015 
Value (£): 
101,007

EPSRC Research Topic Classifications: 
Mathematical Analysis 
Nonlinear Systems Mathematics 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
It is known that for linear elliptic and parabolic equations of second order one can construct monotone functions from the solution. A typical example is the mean value integral of harmonic function over a ball. In this case the mean value integral is monotone function of the radius of the ball. There are more complex examples of this sort such as Almgren's frequency formula which, among other things, helps to identify the structure of the zero set of harmonic function. The aim of this project is to construct monotone functions for the solutions of some nonlinear equations. The choice of this type of operators is adequate since there are various physical problems where the nonlinear equations emerge. For instance, the flow of nonNewtonian fluids with power law dependence of the shear tensor from the velocity, the flow of gas in porous media in turbulent regime, the quantum field theory and the interaction of two biological groups without selflimiting. We aim to construct monotone functions for three free boundary problems with nonlinear governing equations and point out some applications in stochastic game theory (TugofWar model), Chemical Kinetics and Combustion (smouldering of cigarettes and flame propagation).

Key Findings 
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk

Potential use in nonacademic contexts 
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk

Impacts 
Description 
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk 
Summary 

Date Materialised 


Sectors submitted by the Researcher 
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk

Project URL: 

Further Information: 

Organisation Website: 
http://www.ed.ac.uk 