ATMW Partial differential equations of fractional order (2015)

Venue: T.I.F.R,  Bangalore­
Dates:  06th ­-18th July , 2015


Convener(s) Speakers, Syllabus and Time table Applicants/Participants


School Convener(s)

Name Imran Biswas

 K. Sandeep

Mailing Address T.I.F.R Centre for Applicable Mathematics,
Post Bag no. 6503, Sharada Nagar, Yelahanka New town, Bangalore­ 560065
T.I.F.R Centre for Applicable Mathematics,
Post Bag no. 6503, Sharada Nagar, Yelahanka New town, Bangalore­ 560065


Speakers and Syllabus 

The workshop was conducted at TIFR Centre for applicable mathematics, Bangalore during  July 06­18, 2015. The response to our call for participation was very satisfying and we received seventy three applications and we could only select thirty of them, as planned in our original  proposal. The final number of outstation participants stood at twenty even and there was about  ten local participants as well. The programme was intended to introduce the theory of fractional order partial differential equations, an active area of research. The focus was to familiarise and  emphasise on the basics of the subject to the participants. 
The first week was primarily devoted to build the necessary background in aspects of analysis  which are essential for this subject. A number of important topics were discussed. The  fractional order Sobolev spaces were introduced and their main properties like compactness,  embeddings, density properties, etc. were taught in detail. In addition, in another series of  lectures, a comprehensive theory of pseudo differential operators were developed and it  included the aspects of tempered distributions and Fourier analysis. Moreover, aspects of  calculus of variations with connections to fractional order PDEs was discussed. 
Large part of second week was devoted to more specific problems involving fractional order  PDEs. The fractional Laplace operator was introduced and issues like their solvability,  maximum principle, etc., were discussed in detail. In addition, this subject has strong  connection with stochastic analysis and control theory. This particular connection was explored  in details in a separate series of lectures and particular emphasis was given on viscosity  solutions for such problems and its application on stochastic control problem . Another topic  covered was the uniqueness of positive solutions of a semilinear fractional order pde. One of  the recent and most difficult result proved in recent times was discussed.
All these courses were supported by tutorials covering exercises and and some of the  preliminary materials.

List of Speakers and topics covered :

  1. Prof. Adimurthi , TIFR­CAM, Bangalore. ( AM)
    Various definitions of Fractional order Sobolev spaces, Sobolev inequalities, compactness, density properties, maximum principle, application to symmetry properties.
  2. Dr. Imran Biswas, TIFR­CAM, Bangalore. ( IB)
    Stochastic analysis, control theory, connection with fractional order equations, viscosity  solutions.
  3. Prof. KT Joseph, TIFR­CAM, Bangalore. (KTJ)
    Definition and basic properties of Pseudo differential operators, calculus of pseudo differential operators, asymptotic expansion of symbols, Schwartz kernel, oscillatory integrals, algebraic structures, continuity properties in Sobolev spaces, elliptic operators, Microlocal analysis.
  4. Prof. K. Sandeep, TIFR­CAM, Bangalore. (KS)
    Semilinear fractional order pde, existence of solutions, symmetry of positive solutions, ground state solutions and their Morse index, uniqueness of ground state solutions.
  5. Dr. Saugata Bandyopadhyay, IISER Kolkata. (SB)
    Various notions of convexities, classification of quasi convexity, minimizers for variational integrals, existence and uniqueness.
  6. Dr. Venky Krishnan, TIFR­CAM, Bangalore. (VK)
    Definition and properties of distributions, tensor product of distributions, Fourier transform, Riesz potential, convolution, wavefront set,Radon Transform, Inverse Radon transform, application to image reconstruction problems.


Course Associates :

  1. Arka Malik, TIFR­CAM, Bangalore. (AMa)
  2. Debabrata Karmakar, TIFR­CAM, Bangalore. (DK)
  3. Indranil Chowdury, TIFR­CAM, Bangalore. (IC)
  4. Manmohan Vashisth , TIFR­CAM, Bangalore. (MV)



   Lecture 1 Tea Lecture 2 Lunch Lecture 3 Tea & Snacks Tutorial
Day Date 9.00­10.30               11.00 ­12.30   2.00 – 3.30               4.00 – 5.00
Mon 06/07 VK SB   AM DK, MV
Tue 07/07 VK AM   VK AMa, MV
Wed 08/07 SB AM   VK DK, MV
Thu 09/07 VK SB   VK AMa, IC
Fri 10/07 SB AM   SB DK, AMa
Sat 11/07 AM SB   KTJ AMa, IC
Mon 13/07 IB AM   KS DK, IC
Tue 14/07 KTJ IB   KS AMa, IC
Wed 15/07 AM KTJ   IB DK, IC
Thu 16/07 IB KS   KTJ AMa, DK
Fri 17/07 KTJ IB   KS DK, IC
Sat 18/07 KS KTJ   IB AMa, IC


Actual Participants


Sr SID Full Name Gender Affiliation State Position in College/ University University /Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D. Deg Date
1 103 Mr. Balraj Durai Samy Male Bharathidasan University Tamil Nadu PhD Bharathidasan University 2011  
2 111 Dr. Rajesh Kumar Gupta Male Thapar University, Patiala Punjab Asst. Prof. Guru Jambheshwar University, Hisar 2001 Oct 10, 2007
4 243 Mr. Jitendra Kumar Dubey Male BANARAS HINDU UNIVERSITY Uttar Pradesh PhD M.Sc. 2012  
5 293 Mr. Vivek Kumar Male IIT Roorkee Uttarakhand/ Uttaranchal Phd DDU Gorakhpur University, Gorakhpur 2013  
6 308 Mr Prasanta Kumar Barik Male IIT ROORKEE Uttarakhand/ Uttaranchal Research Scholar, Ph.D Ravenshaw University 2009  
7 439 Mr Channaveerapala Sateesha Male Vijayanagara Sri Krishna Devaraya University Karnataka PhD Davanagere University 2012 May 1, 2014
8 440 Mr. Puneet Kumar Maurya Male Indian School Of Mines Jharkhand PhD Banaras Hindu University, Varanasi 2012  
9 461 Mr. Anuj Kumar Male Banaras Hindu University Uttar Pradesh PhD CSJMU, Kanpur 2008  
10 526 Ms. Tuhina Mukherjee Female Indian Institute Of Technology, Delhi Delhi PhD student IIT Guwahati 2014  
11 653 Mr Jayanta Borah Male IIT Guwahati Assam Asst. Prof. Gauhati University 2003  
12 670 Dr. Muthukumar Palanisamy Male Gandhigram Rural Institute - Deemed University Tamil Nadu Assistant Professor Bharathiar University, Coimbatore 2002 Dec 22, 2010
13 765 Mr. Gaurav Dwivedi Male IIT Gandhinagar Gujarat PhD IIT Delhi 2010  
14 885 Mr. Ram Baran Verma Male IIT Gandhinagar Gujarat PhD University of Allahabad 2011  
15 950 Mr. Pawan Kumar Mishra Male IIT Delhi Delhi PhD IIT Delhi 2012  
16 1597 Ms. Sangita Choudhary Female Department of Mathematics,
Savitribai Phule Pune University
Maharashtra Research Student (Completed M.Phil) Savitribai Phule Pune University 2012  
17 1625 Ms Sandhyatai Digambarrao Kadam Female Swami Ramanand Teerth Marathwada University Maharashtra Ph.D(Research Student) Swami Ramanand Teerth Marathwada University 2013  
18 1743 Mr Akash Ashirbad Panda Male Indian Institute of Science Education and Research, Thiruvananthapuram Kerala Integrated PhD Student IISER, TVM Awaiting Result  
19 1749 Mr Saurav Samantaray Male Indian Institute of Science Education and Research, Thiruvananthapuram Kerala Integrated PhD Student IISER, TVM Awaiting Result  
20 1829 Mr Nimit Rana Male IISER Thiruvananthapuram Kerala MS Student IISER TVM 2015  
21 1883 Ms. Deepika Sirswal Female National Institute of Technology,Kurukshetra (Haryana). Haryana Research Scholar Kurukshetra University, Kurukshetra. 2012  
22 2170 Ms Debangana Mukherjee Female IISER PUNE Maharashtra PHD MOUNT CARMEL COLLEGE, BANGALORE 2013  
23   Ms. Neetu Garg   NIT, Kurukshetra          

In addition to this list, around 10 local participants also attended the programme.


 How to reach TIFR, Bangalore

* From Bangalore Internation Airport (Distance 28km)

You can hire a City taxi or private taxi from Airport to TIFR , Yelahanka new town.
Landmark : Yelahanka new town Dairy Circle

* From Bangalore City Railway Station or Majestic Bus Stand (Distance 16km)

You can hire a City Taxi or Auto Rickshaw and ask drop for Yelahanka new town. The fare for City Taxi will be approximately Rs.400. For Auto Rickshaw fare will be approximately Rs.200.

You can also use BMTC Bus service to reach TIFR. You can board into following buses which comes to Yelahanka new town bus stand.

Buses to Yelahanka new town : 402B, 402D, 284D

TIFR CAM is located walkable distance from Yelahanka new town bus stand.

You may also visit the link below for links to the route maps.