9Ef 4 PAG - '- " " " " - '' " - ilt ELECTF. Afl... ~~O. ON PAGE. Form Appove. 121 Ayers Hall AFOSR-TR Knoxville, TN I

Transcription

1 9Ef 4 ON PAGE. Form Appove. Afl... ~~O PAG AD-A250 I I l 1111I! II 549 lii age o oo, - '- " " " " - '' " - MB No " hour per response, ind t.e time for n data sources. he Inhmi ollection of information. s omments shi~to, rring rieamauarter this burden Services. estimate Orectorate or any Tor other Information aspect Operations of this and Report. 12 efferson I n' iu kqement and Budget. Paperwork Reduction Protct ( ), Wa hington, DC AI R P RTT PE A D'eESC VE E.AI 1 nl1 Apr Sep TITLE AND SUBTITLE S. FUNDING NUMBERS "NON-CONVEX PROBLEMS IN PDE: EQUILIBRIUM THEORY AND DYNAMICS" (U) 6. AUTHOR(S) Prof Nicholas Alikakos ilt ELECTF ll F 2304/CS 7. PEFORMIG NAE(S) ORGNIZATON c~ax3. PERFOMG11111 ORGANIZATION University of Tennessee _ REPIT NUMBER Dept of Mathematic s 121 Ayers Hall AFOSR-TR Knoxville, TN SPONSORING /MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING MONITORING ' AFOSR/NM AGENCY REPORT NUMBER Bldg 410 Boiling AFB DC AFOSR SUPPLEMENTARY NOTES 12a. DISTRIBUTION / AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE Approved for public release; Distribution Unlimited UL 13. ABSTRACT (Maximum 200 words) The main goal of the research discussed in this conference is a mathematical understanding of nonlinear dynamics appropriate for models of continua which admit phase transitions. The mathematical problems that were discussed addressed the general quastions. How do nonlinear systems relax to equilibrium? How do interfaces and transition zones propagate? The speakers represented different aspects of the subject. The group included theoreticians as well as numerical analysts. The conference was very well attended and quite successful. 14. SUBJECT TERMS IS. NUMBER Of PAGES PRICE CODE 17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT OF REPORT OF THIS PAGE OF ABSTRACT UNCLASS IFIED UNCLASSIFI ED UNCLASS IFIED SAR "* - -C Sa-CCa, :O 298 (Rev 2-89) 29S-C-;

2 Final Report on AFOSR The main goal of the research discussed in this conference is a mathematical understanding of nonlinear dynamics appropriate for models of continua which admit phase transitions. The mathematical problems that were discussed add'ressed the general questions. How do nonlinear systems relax to equilibrium? How do interfaces and transition zones propagate? The speakers represented different aspects of the subject. theoreticians as well as numerical analysts. The group included The conference was very well attended and apparently quite successful. On behalf of the Mathematics Department here at UT I want to express our thanks to the Air Force that made this possible. Please find enclosed: 1. Program of talks and lecturers 2. List of supported participants 3. Bills from hotels. A-oj~e.3Io&~ For 0 vdtstrtbulis1/ AvaaIbIaiS 0.6. Dist ~ an-d or Speclal

3 BARRETT MEMORIAL LECTURES TENTATIVE PROGRAM UNIVERSITY CENTER - SHILOH ROOM THURSDAY. APRIL 4 9:15 Introductory Remarks 9:30-10:30 J. Ball, Heriot-Watt University Nonattainment of the minimum in the Calculus of Variations 12:00-2:00 Lunch Break 2:00-3:00 L.C. Evans, Berkeley Phase Transitions and Wave front Propagation I 3:00-3:15 Break 3:15-4:15 J. Sethian, Berkeley Fronts and Interfaces: Computing Snowflakes, Flames, and Fluids ,r I111O1I

4 BARRETT MEMORIAL LECTURES TENTATIVE PROGRAM UNIVERSITY CENTER - SHILOH ROOM FRIDAY. APRIL 5 9:30-10:30 J. Ball, Heriot-Watt University Crystal microstructure via elasticity theory 10:30-11:00 Break 11:00-12:00 P. Fife Dynamical Aspects of the Cahn - Hilliard Equation: Stationary states and their instabilities 12:00-2:00 Lunch Break 2:00-3:00 L.C. Evans, Berkeley Ti&: Phase Transitions and Wave front propagation II 3:00-3:15 Break 3:15-4:15 G. Fusco, Rome Tle~: Slow Dynamics for the Cahn - Hilliard Equation in higher space dimensions

5 BARRETT MEMORIAL LECTURES TENTATIVE PROGRAM UNIVERSITY CENTER - SHILOH ROOM SATURDAY. APRIL 6 9:30-10:30 J. Ball, Heriot-Watt University Dynamics and Minimizing Sequences 10:30-11:00 Break 11:00-12:00 P. Fife Titl: Dynamical Aspects of the Cahn - Hilliard Equation: Layered Solutions 12:00-2:00 Lunch Break 2:00-3:00 L.C. Evans, Berkeley i&: Phase Transitions and Wave front propagation IlI 3:00-3:15 Break 3:15-4:15 S.B. Angenent, University of Wisconsin, Madison M, I : Anisotropic Motion of a phase interface

6 Barrett Lectures, 4/91 aici Univrsity Hotel Accommodations W. McKinney NC State $ Dan and Pat Phillips Purdue R. Gardner U. of Massachusetts W. Heinz Georgia Tech P. Bates Brigham Young J. Ward U. of Alabama, Birmingham G. Fusco Rome J. Ball Heriot-Watt L.C. Evans Berkeley P. Fife University of Utah S. Angenent U. of Wisconsin, Madison J. Sethian Berkeley K. Lu and G. Xun Brigham Young Tataru Georgia Tech C. Li University of Pennsylvania S. Koike Berkeley K. Michaikov Georgia Tech Tetseu S. Sritharan U. of California, Riverside P. Sternberg University of Indiana 76.00

7 Barrett Lectures, 4/91 Participants University Hotel Accommodations J. Mu Georgia Tech D. Eyre University of Utah I 4.00 L. Li University of Kansas M. James University of Minnesota R. Gariepy University of Kentucky J. Arrieta Georgia Tech A. Burchard Georgia Tech J. Parish University of Maryland J. Anderson Tennessee College D. Adams University of Kentucky W. Shen Indiana University H. Leiva Georgia Tech J. Lewis University of Kentucky Rodriguez-Bernal Georgia Tech Carvalho University of Maryland E. Van Vleck Georgia Tech Smith Arizona State University J. Hale Georgia Tech B. Vernescu Courant S. Alama Georgia Tech

8 PatcpnsUniversity Hotel Accommodations R. Peszek U. of Maryland C. Cosner and S. Cantrell University of Miami M. Katsoulakis Brown University C. Calderer Carnegie Mellon