Partial Differential Equations (2022) | National Centre for Mathematics

Convener(s)


Name:	Dr. Ram Prakash Sharma, Dean (SA)	Prof. G.D. Veerappa Gowda
Mailing Address:	Department of Mechanical Engineering, NIT Arunachal Pradesh-791113	Former Professor TIFR Centre for Applicable Mathematics Sharadanagar, Chikkabommasandra Yelahanka New Town, Bangalore - 65.
Email:	rpsharma at nitap.ac.in, rpsharma.research at gmail.com	gowda at tifrbng.res.in

Partial differential equations (PDEs) are used to mathematically formulate many physical phenomena which involves functions of several variables, for example arising in fluid flow, propoagation of heat or sound wave, elasticity,electromagnetism, image processing,.etc. PDEs also arise in geometric problems. Three fundamental equations, Laplace, wave and heat equation with their generalization, in additions to first order linear and non-linear PDEs are considered. Importance are given to derive formula for solutions in the classical sense in addition to studying existence, uniqueness and properties of solutions like, regularity and maximum principle. The topics to be covered in the workshop are arranged in such a way that the university and college teachers get exposed to a good mix of classical theory and modern approaches.

Please note that TEW is meant only for the local college teachers. The lectures in this workshop covers specific topics which are relevant for the teacher's classroom instructions. The usual length of the TEW is 5/6 days. An important component of this programme is the discussion hour during which the teachers will have opportunities to get their doubts cleared.

Dates:

Thursday, February 17, 2022 - 19:00 to Sunday, March 13, 2022 - 19:00

Venue:

Online Mode

Venue Address:

National Institute of Technology Arunachal Pradesh Jote, District: Papum Pare
Arunachal Pradesh-791113

Venue State:

Arunachal Pradesh

Venue City:

PIN:

791113

Chrono Order:

386

Syllabus:

Name of the Speaker with affiliation	No. of Lectures (each of 1.5 hours)	Detailed Syllabus
Veerappa Gowda G. D., Former Professor, TIFR-Centre for Applicable Mathematics, Bengaluru	4	Introduction to PDE. Solving linear, semi-linear, quasilinear and fully non-linear first order equations by using the method of characteristics. Conservation laws: Weak Solutions, concept of entropy solution and Riemann problems. Examples with their applications in various fields.
Prof. Ujjwal Koley (UK) , Associate Professor at TIFR-CAM	4	Laplace equation: Fundamental solution, mean-value property, strong maximum principle. Introduction to Sobolev spaces, notion of weak derivatives. Poisson equation: Notion of weak solution, Lax-Milgram Lemma, existence and uniqueness of the weak solution for Dirichlet as well as Neumann problems.
Joseph K.T., Former Professor, TIFR-Centre for Applicable Mathematics, Bengaluru	4	Wave equation:Geometrical and symmetry properties of the wave operator, properties of the fundamental solution, the well-posedness and properties of the solution such as , energy conservation, loss of regularity in the solution, finite speed of propagation and Huygen's principle. Second order linear hyperbolic equations with variable coefficients: Existence, uniqueness of the solution and its continuous dependence on the data. Regularity results and the finite speed of propagation property.
Venky Krishnan, TIFR-Centre for Applicable Mathematics, Bengaluru	4	Heat Equation: Introduction to the heat equation and derivation of the fundamental solution. Solution to the homogeneous problem and solution to the non-homogeneous problem by Duhamel's principle. Regularity of the solution in bounded domains and explanation of the infinite speed propagation. Heat mean value formula. Weak and strong maximum principles. Energy methods to prove the uniqueness and backward uniqueness of the solution.

References:

(1) Evans, L.C., Partial differential equations, Rhode Island: AMS, Providence.

(2) Folland, G.B., Introduction to partial differential equations,2nd ed., Princeton University Press.

(3) John, F., Partial Differential equations, Springer verlag.

(4) Jurgen Jost, Partial differential equations, Springer

(5) McOwen, R.C., Partial differential equations:Methods and Applications, 2nd ed.,Pearson Education.

Name of the tutors:

S. No.	Name	Affiliation
1	Joseph K.T.	Former Professor, TIFR-Centre for Applicable Mathematics, Bengaluru
2	Ujjwal Koley	Associate Professor at TIFR-CAM
3	Veerappa Gowda G. D.	Former Professor, TIFR-Centre for Applicable Mathematics, Bengaluru
4.	Venky Krishnan	TIFR-Centre for Applicable Mathematics, Bengaluru

Time Table:

Week-1, February (17,18,19,20)

	Lecture-1	Lecture-2	Lecture-3	Lecture-4	Tutorial-1	Tutorial-2
Date	Thursday 17-02-2022	Friday 18-02-2022	Saturday 19-02-2022	Saturday 19-02-2022	Sunday 20-02-2022	Sunday 20-02-2022
Time	18:00-19:30	18:00-19:30	16:00-17:30	18:00-19:30	16:30-17:30	18:00-19:00
Speaker	GDVG	UK	GDVG	UK	GDVG	UK

Week-2, February (24,25,26,27)

	Lecture-1	Lecture-2	Lecture-3	Lecture-4	Tutorial-1	Tutorial-2
Date	Thursday 24-02-2022	Friday 25-02-2022	Saturday 26-02-2022	Saturday 26-02-2022	Sunday 27-02-2022	Sunday 27-02-2022
Time	18:00-19:30	18:00-19:30	16:00-17:30	18:00-19:30	16:30-17:30	18:00-19:00
Speaker	UK	GDVG	UK	GDVG	UK	GDVG

Week-3, March (3,4,5,6)

	Lecture-1	Lecture-2	Lecture-3	Lecture-4	Tutorial-1	Tutorial-2
Date	Thursday 03-03-2022	Friday 04-03-2022	Saturday 05-03-2022	Saturday 05-03-2022	Sunday 06-03-2022	Sunday 06-03-2022
Time	18:00-19:30	18:00-19:30	16:00-17:30	18:00-19:30	16:30-17:30	18:00-19:00
Speaker	KTJ	VK	KTJ	VK	KTJ	VK

Week-4, March (10,11,12,13)

	Lecture-1	Lecture-2	Lecture-3	Lecture-4	Tutorial-1	Tutorial-2
Date	Thursday 10-03-2022	Friday 11-03-2022	Saturday 12-03-2022	Saturday 12-03-2022	Sunday 13-03-2022	Sunday 13-03-2022
Time	18:00-19:30	18:00-19:30	16:00-17:30	18:00-19:30	16:30-17:30	18:00-19:00
Speaker	VK	KTJ	VK	KTJ	VK	KTJ

Full forms for the abbreviations of speakers and tutors:

UK:Ujjwal Koley

KTJ: Joseph K.T.

VK: Venky Krishnan

GDVG: Veerappa Gowda G D

Selected Applicants:

Sr.	SID	Full Name	Gender	Affiliation	Position in College /University	University/ Institute M.Sc./ M.A.	Year of Passing M.Sc./ M.A	Ph.D. De Date
1	37771	Mr. Md Hasanuzzaman	Male	ALIGARH MUSLIM UNIVERSITY	PhD	ALIGARH MUSLIM UNIVERSITY	2015
2	37777	Mr. Firdous Ahmad Mala	Male	Government Degree College Sopore	Assistant Professor	University of Kashmir	2007
3	37780	Mr. Ganesh Jayantrao Dharmadhikari	Male	IGNOU	PGDAST STUDENT	IISER TVM	2020
4	37784	Mrs. Renu Gill	Female	Banasthali vidyapeeth, Rajasthan	PhD	Banasthali Vidyapith, Rajasthan	2016
5	37923	Ms Ekta Jain	Female	University of delhi	Research scholar	University of delhi	2014
6	37930	Mr. N Subbarayudu	Male	Sri Venkateswara University	PhD	Yogi Vemana University	2016	26/08/2020
7	37958	Mr. Shubham Garg	Male	IIT Jodhpur	PhD	IIT Ropar	2019
8	37969	Dr. Kuldip Katiyar	Male	Chandigarh University	Asso. Prof	MJP Rohilkhand University, Bareilly	2006	13/06/2017
9	38020	Dr. Shiv Kumar Kumar Sharma	Male	Chandigarh University	Associate Professor	DBRAU Agra	2004	21/07/2017
10	38090	Mr Bala Samuvel J	Male	ALPHA ARTS AND SCIENCE COLLEGE	Assistant Professor	M.Sc.	2013
11	38104	Dr. Balaji Padhy	Male	Centurion University	Asst.Prof.	Berhampur University	2008	10/12/2021
12	38108	Mr Arabinda Pandab	Male	PATTAMUNDAI COLLEGE	LECTURER IN MATHEMATICS	UTKAL UNIVERSITY, VANI VIHAR,ODISHA	1996
13	38113	Mr Aamer Suhail Mohammad Mustafa Pathan	Male	N.E.S. SCIENCE COLLEGE NANDED	Research Scholar	Swami Ramanand Teerth Marathwada University Nanded	2019
14	38128	Mr Rahul Bhardwaj	Male	Indian Institute of Technology Jammu	PhD	Indian Institute Of Technology Kanpur	2018
15	38131	Mr. Surath Ghosh	Male	Jecrc University	303905	Visva Bharati	2015	01/10/2021
16	38137	Mr Venkata Ramanaraju J	Male	School of Sciences, Jain deemed-to-be University	Assistant Professor	Karnatak University	2000
17	38205	Dr. Kalu Ram Meena	Male	Acharya Narendra Dev College, University of Delhi	Assistant Professor	IIT Kharagpur	2012	12/10/2018
18	38228	Mr. Mohit Malik	Male	NIFTEM	PhD	DCRUST	2018
19	38236	Dr. Raja N	Male	KPR Institute of Engineering and Technology	Assistant Professor (Sr.G)	M.Sc	2011	22/07/2019
20	38244	Mr. Tapas Ranjan Panigrahi	Male	BITS-PILANI, HYDERABAD CAMPUS	PhD	Utkal University, Vanivihar	2012
21	38246	Dr Tanuku Poorna Kantha	Female	GVP COLLEGE OF ENGINEERING FOR WOMEN	ASSISTANT PROFESSOR	ANDHRA UNIVERSITY	1999	30/04/2010
22	38247	Dr. Sanchita Sarkar	Female	NSHM Knowledge Campus Durgapur	Professor	M.Sc	2001	10/05/2014
23	38248	Dr. Robin Singh	Female	Graphic Era Hill University Dehradun	Associate Professor	M.Sc		30/11/2015
24	38264	Dr Yogendra Kumar Sharma	Male	Manav Rachna University, Faridabad, India	Faculty Of Mathematics	M.Sc from Ch. Chran singh University, Meerut, U P	1994	20/08/2003
25	38274	Ms Lhinghoineng Kipgen	Female	Department of mathematical science, delhi University	Phd student	Delhi University	2015
26	38283	Ms Divya G	Female	IIT Tirupati	PhD student	Bangalore University	2016
27	38286	Mr Sankar S	Male	Periyar University	Research Scholar	Bharathidasan University	2017
28	38294	Dr Amit Kumar Saraswat	Male	GLA University	Assistant professor	Agra University	2000	10/07/2017
29	38295	Mr. Bipin Kumar Chaudhary	Male	UNIVERSITY OF DELHI	PhD	University of Allahabad, M.Sc.	2017
30	38297	Mr Gautamprasad Vishnuprasad Patel	Male	Hasmukh Goswami College of Engineering	Ass. Prof.	The Maharaja Sayajirao University of Baroda	2009
31	38302	Ms. Saloni Gupta	Female	iit jodhpur	Research assistant jrf	Iit gandhinagar	2019
32	38306	Mr. Sushil Singla	Male	Shiv Nadar University, Delhi NCR, India.	PhD	Shiv Nadar University Delhi NCR	2016
33	38313	Mr. Om Prakash	Male	JECRC University	Assistant Professor	Dr. Bhim Rao Ambedkar University Agra	2011
34	38314	Mr Shaik Shafi	Male	National Institute of Technology Arunachal Pradesh	791123	Kakatiya University M.Sc	2017
35	38315	Mr Sunendra Shukla	Male	NIT ARUNACHAL PRADESH	Ph.D STUDENT	MADHYA PRADESH BHOJ OPEN UNIVERSITY BHOPAL	2020
36	38322	Ms. Puspanjali Jena	Female	Siksha O Anusandhan (Deemed to be university)	PhD	Berhampur University, Odisha.	2014
37	38323	Mr Prakash Kumar Ratha	Male	Siksha 'O' Anusandhan (Deemed to be University)	PhD	Orissa University of Agriculture and Technology	2017
38	38331	Dr. Santosh Kumar Bhal	Male	Centurion University of Technology and Management	Assistant Professor	Utkal University	2005	08/09/2020
39	38333	Ms Rajni Gupta	Female	St. Stephen's College, University of Delhi	Assistant Professor	Kirorimal College, University of Delhi	2014
40	38339	Dr Swati Agarwal	Female	Mangalayatan University	Assistant Professor	St. John's College (Dr. Bhimrao Ambedkar University), Agra	2011	11/01/2019
41	38342	Ms. Pooja Yadav	Female	Department of Mathematics Delhi University	MSc Student	Dehli University	Appeared / Awaiting Result
42	38344	Mr. Debasish Gorai	Male	NIT, ARUNACHAL PRADESH	Ph.D.	THE UNIVERSITY OF BURDWAN	2017
43	38347	Mr. Abhishek Sharma	Male	Govt. PG college, Dholpur	Msc Student	Govt. PG college, Dholpur	Appeared / Awaiting Result
44	38348	Mr. Saurabh Bansal	Male	Iit Guwahati	Phd Student	Iit Bombay	2020
45	38354	Dr. Minto Rattan	Male	University Institute of Engineering and Technology, Panjab University	Assistant Professor	M. Sc.	2001	20/12/2010
46	38356	Dr. Seema Tinker	Female	JECRC University, Jaipur	Asso. Prof.	University of Rajasthan	2002	12/04/2006
47	38357	Mr Avdesh Bajpayee	Male	Govt. PG college Dholpur	Msc Student	Govt. PG college Dholpur	Appeared / Awaiting Result
48	38358	Mrs Swati Mohanty	Female	siksha O Anusandhan(Deemed to be university)	PhD student	Sambalpur university	2017
49	38362	Ms. Sanwatee Behera	Female	SIKSHA O ANUSANDHAN (DEEMED TO BE UNIVERSITY), BHUBANESWAR,ODISHA	PhD STUDENT	ORISSA UNIVERSITY OF AGRICULTURE AND TECHNOLOGY, BHUBANESWAR, ODISHA	2019
50	38363	Prof Dr Yogesh Sharma	Male	MAHILA P.G COLLEGE,JODHPUR	ASSISTANT PROFESSOR	Jai narayanan Vyas University Jodhpur	1997	28/02/2001
51	38369	Mr Vijaykumar Dattatry Mathpati	Male	N. E. S. Science college Nanded	Phd student	Science college Nanded	2018
52	38378	Mr. Vishalsingh Sarjeetsingh Chauhan	Male	DIEMS, Aurangabad	Ass Prof	Pune University	2007
53	38402	Dr. Ramesh Chand	Male	ABV Govt. College Bangana	Associate Professor	HP University Shimla	1995	01/10/2001
54	38403	Mrs Sushree Sangita Acharya	Female	Siksha o Anusandhan (Deemed to be university)	Phd	Centurion University
55	38406	Prof. Manish Goyal	Male	GLA University, Mathura (U.P.) India	Professor	Dr. Bhimrao Aambedkar University, Agra	1999	30/01/1999
56		Kirnu Badak
57		Chandralekha Mahanta		NIT Arunachal Pradesh	Research Scholar
58		Parshuram sahoo
59		Rashmi Agarwal
60		Sushama Baag

How to Reach:

TBA

School Short Name:

pde

Last Date Application:

Wednesday, December 15, 2021

School Type:

TEW