紀要論文

紀要論文

text

2007-03

Osaka Journal of Mathematics. 2007, 44(1), p. 197-205

Representation formulas of the solutions to the Cauchy problems for first order systems

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2007-03

Representation formulas of the solutions to the Cauchy problems for first order systems of the forms ∂u/∂t - Σ_(j=1)^(d)A_j(t)∂u/∂x_j - A_0(t)u = f are established. The coefficients A_j's are assumed to be matrix-valued functions of the forms A_j(t) = α_j(t)I +?β_j(t)M_j, where α_j (t),β_j(t), j = 1,...,d, are real-valued continuous functions, the eigenvalues of the matrices M_j, j = 1,...,d, are real, and the commutators [M_j, M_l] = 0 for all j, l = 0, 1,...,d. No restrictions on the multiplicities of the characteristic roots are imposed.

10.18910/4372

4372

Representation formulas of the solutions to the Cauchy problems for first order systems

Osaka University and Osaka City University, Departments of Mathematics

英語

2007-03

Osaka Journal of Mathematics

44

1

197

205

https://hdl.handle.net/11094/4372

10.18910/4372

https://doi.org/10.18910/4372