Geodesic
Controllable systems of partial differential equations
Applications of Mathematics, Tome 31 (1986) no. 1, pp. 41-53

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In the paper definitions of various kinds of stability and boundedness of solutions of linear controllable systems of partial differential equations are introduced and their interconnections are derived. By means of Ljapunov's functions theorems are proved which give necessary and sufficient conditions for particular kinds of stability and boundedness of the solutions.
In the paper definitions of various kinds of stability and boundedness of solutions of linear controllable systems of partial differential equations are introduced and their interconnections are derived. By means of Ljapunov's functions theorems are proved which give necessary and sufficient conditions for particular kinds of stability and boundedness of the solutions.
DOI : 10.21136/AM.1986.104183
Classification : 35B35, 35B37, 93C05, 93C20, 93D05
Keywords: stability; boundedness; controllable system of partial differential equations; Ljapunov's function 
Tumajer, František. Controllable systems of partial differential equations. Applications of Mathematics, Tome 31 (1986) no. 1, pp. 41-53. doi: 10.21136/AM.1986.104183
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[1] H. П. Соколов: О функциях от многомерных матриц и примении их к решению линейных систем дифференциальных уравнений с частными производными. УМЖ, т. 22, No. 6, 1970, 769-782. | Zbl

[2] J. Kučera I. Vrkoč: Note on stability of a linear homogeneous control system. Časop. pěst. mat. 95 (1970), 56-61. | MR

[3] F. Tumajer: Ljapunov's method in the theory of the boundedness of linear control flows. (Czech.) Časop. pěst. mat. 98 (1973), 278-284. | MR

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