- Email: [email protected]
Reply to letter by Jane Cronin (1982)
Bulletin of Mathematical Biology, Vol. 44, No 3, p. 450, 1982 Printed in Great Britain.
0092-82401821030450~d1503,0010 Pergamon Press Ltd Society for Mathematical Biology
L E T T E R TO T H E E D I T O R REPLY TO LETTER BY JANE CRONIN (1982)
• 1. S. ZHITOMIRSKYand A. A. KAGNA Physico Technical Institute of Low Temperature, Academy of Sciences of the Ukrainian S.S.R., Kharkov, U.S.S.R. It is difficult not to agree with the remarks by Dr. Cronin. At present, the improperly posed problems attract special interest of mathematical physicists since they may play a significant role in solving many applied problems. The improperly posed problems could be separated into three classes: (1) those having no solution; (2) those with more than one solution; and (3) those with a solution instable with respect to varying initial data (numerical factors, initial and boundary conditions etc.). It is the problems of the third type that are the most important in practice. We cannot speak about an adequate mathematical description of physical processes if the resulting mathematical problems do not have solutions. In the case of a non-unique solution, one usually seeks additional criteria to obtain a physically realizable solution.
450
0092-82401821030450~d1503,0010 Pergamon Press Ltd Society for Mathematical Biology
L E T T E R TO T H E E D I T O R REPLY TO LETTER BY JANE CRONIN (1982)
• 1. S. ZHITOMIRSKYand A. A. KAGNA Physico Technical Institute of Low Temperature, Academy of Sciences of the Ukrainian S.S.R., Kharkov, U.S.S.R. It is difficult not to agree with the remarks by Dr. Cronin. At present, the improperly posed problems attract special interest of mathematical physicists since they may play a significant role in solving many applied problems. The improperly posed problems could be separated into three classes: (1) those having no solution; (2) those with more than one solution; and (3) those with a solution instable with respect to varying initial data (numerical factors, initial and boundary conditions etc.). It is the problems of the third type that are the most important in practice. We cannot speak about an adequate mathematical description of physical processes if the resulting mathematical problems do not have solutions. In the case of a non-unique solution, one usually seeks additional criteria to obtain a physically realizable solution.
450