|
Integral representation and stabilization of the solution to the Cauchy problem for an equation with two noncommuting operators
A. V. Glushak Voronezh Polytechnic Institute
Abstract:
We obtain an integral representation for the solution to the Cauchy problem
dvdt=B21v+12b(t)(B2B1+B1B2)v+c(t)B22v,v(0)=v0,
where the operators B1 and B2 are the infinitesimal generators of strongly continuous groups and B1B2−B2B1=k1, k≠0. For the case in which k=ik1, k1∈R, it is proved that the solution tends to zero as t→+∞.
Received: 17.02.1993
Citation:
A. V. Glushak, “Integral representation and stabilization of the solution to the Cauchy problem for an equation with two noncommuting operators”, Mat. Zametki, 58:1 (1995), 38–47; Math. Notes, 58:1 (1995), 703–709
Linking options:
https://www.mathnet.ru/eng/mzm2023 https://www.mathnet.ru/eng/mzm/v58/i1/p38
|
Statistics & downloads: |
Abstract page: | 369 | Full-text PDF : | 166 | References: | 38 | First page: | 1 |
|