Undetermined Coefficient Problems for Quasi-Linear Parabolic Equations
Final rept. 1 Jan 1989-30 Sep 1992
TEXAS A AND M RESEARCH FOUNDATION COLLEGE STATION
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Our research efforts during the grant period were concerned with undetermined coefficient problems in partial differential equations focusing on three distinct areas problems where the unknown coefficients depend only on the dependent variables problems giving rise to first order equations where the boundary conditions and the coefficients in the equations have a nonlocal dependence on the variables and inverse spectral problems, in which unknown coefficients have to be determined from eigenvalue data. These problems originate from situations where one wants to recover unknown material properties, or to determine the nature of an unknown physical law. A number of theoretical results existence as well as uniqueness as well as computational algorithms were derived for model elliptic, parabolic and hyperbolic equations. During the period of the grant, two major conferences were organized by the principal investigators, 1 Ph.D. thesis was completed, 17 publications appeared, and an additional 5 manuscripts were submitted.
- Numerical Mathematics