ATMW Partial differential equations of fractional order (2015)
|Dates:||06th -18th July , 2015|
|Convener(s)||Speakers, Syllabus and Time table||Applicants/Participants|
|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
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 :
- Prof. Adimurthi , TIFRCAM, Bangalore. ( AM)
Various definitions of Fractional order Sobolev spaces, Sobolev inequalities, compactness, density properties, maximum principle, application to symmetry properties.
- Dr. Imran Biswas, TIFRCAM, Bangalore. ( IB)
Stochastic analysis, control theory, connection with fractional order equations, viscosity solutions.
- 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.
- 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.
- Dr. Saugata Bandyopadhyay, IISER Kolkata. (SB)
Various notions of convexities, classification of quasi convexity, minimizers for variational integrals, existence and uniqueness.
- 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 :
- Arka Malik, TIFRCAM, Bangalore. (AMa)
- Debabrata Karmakar, TIFRCAM, Bangalore. (DK)
- Indranil Chowdury, TIFRCAM, Bangalore. (IC)
- 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|
|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|
|3||113||Mr Arunagirinathan S||Male||THIRUVALLUVAR GOVT.ARTS COLLEGE||Tamil Nadu||PhD Student||THIRUVALLUVAR GOVT.ARTS COLLEGE,
|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 http://math.tifrbng.res.in/contactus for links to the route maps.