| Title:
|
Generalized solutions of ordinary linear differential equations in the Colombeau algebra (English) |
| Author:
|
Ligęza, Jan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
118 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
123-146 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper first order systems of linear of ODEs are considered. It is shown that these systems admit unique solutions in the Colombeau algebra $\Cal L(\bold R^1)$. (English) |
| Keyword:
|
linear Cauchy problem |
| Keyword:
|
Colombeau algebra of generalized distributions |
| Keyword:
|
existence |
| Keyword:
|
uniqueness |
| Keyword:
|
generalized ordinary differential equation |
| Keyword:
|
Cauchy problem generalized function |
| Keyword:
|
distribution |
| MSC:
|
34A10 |
| MSC:
|
34A12 |
| MSC:
|
34A30 |
| MSC:
|
34G10 |
| MSC:
|
46F05 |
| MSC:
|
46F99 |
| MSC:
|
46N20 |
| idZBL:
|
Zbl 0776.34046 |
| idMR:
|
MR1223478 |
| DOI:
|
10.21136/MB.1993.126054 |
| . |
| Date available:
|
2009-09-24T20:57:50Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126054 |
| . |
| Reference:
|
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| Reference:
|
[2] P. Antosik J. Ligęza: Products of measures and functions of finite variation.In: Proc. of the conference on generalized functions and operational calculus, Varna 1975, Sofia 1979, 20-26. MR 0547326 |
| Reference:
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[3] P. Antosik J. Mikusinski R. Sikorski: Theory of Distributions. The sequential approach.Elsevier-PWN, Amsterodam-Warsaw. MR 0365130 |
| Reference:
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[4] J. F. Colombeau: Elementary Introduction to New Generalized Functions.North Holland, Amsterodam, New York, Oxford, 1985. Zbl 0584.46024, MR 0808961 |
| Reference:
|
[5] J. F. Colombeau: A multiplication of distribution.Jour. of Math. Anal. and Appl. 94 (1983), 96-115. MR 0701451, 10.1016/0022-247X(83)90007-0 |
| Reference:
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| Reference:
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| Reference:
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| Reference:
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[9] J. Kurzweil: Generalized ordinary differential equations.Czechoslov. Math. Jour. 8 (1958), 360-389. Zbl 0102.07003, MR 0111878 |
| Reference:
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[10] J. Kurzweil: Generalized ordinary differential equations and continuous dependence on a parameter.Czechoslov. Math. Jour. 7(1957), 418-449. Zbl 0090.30002, MR 0111875 |
| Reference:
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[11] J. Kurzweil: Linear differential equations with distributions as coefficients.Bull. Acad. Polon. Sci. Ser. Sci. Mat. Astronom. Phys. 7 (1959), 557-580. Zbl 0117.34401, MR 0111887 |
| Reference:
|
[12] A. Lasota J. Traple: Nicoletti boundary value problem for system of linear differential equations with distributional perturbations.Prace Mathematyczne Uniwersytetu Jagiellonskiego, Kraków 15(1971), 103-108. MR 0369785 |
| Reference:
|
[13] J. Ligęza: On distributional solutions of some systems of linear differential equations.Časopis pro pěstování mat. 102 (1977), 37-41. MR 0460757 |
| Reference:
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[14] J. Ligęza: Weak solutions of ordinary differential equations.Prace Naukowe Uniwersytetu Slaskiego, Katowice 842 (1986). MR 0868863 |
| Reference:
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[15] J. Persson: The Cauchy problem for linear distribution differential equations.Funkcial. Ekvac. 30 (1987), 163-168. Zbl 0643.34004, MR 0915270 |
| Reference:
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[16] R. Pfaff: Generalized systems of linear differential equations.Proc. of the Royal Soc. of Edingburh, S. A. 89(1981), 1-14. Zbl 0475.34005, MR 0628123 |
| Reference:
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[17] Š. Schwabik M. Tvrdý O. Vejvoda: Differential and Integral Equations.Praha, 1979. MR 0542283 |
| Reference:
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[18] Š. Schwabik: Generalized differential equations.Rozp. Česk. Akad. Věd. 956(1985). Zbl 0594.34002 |
| Reference:
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[19] L. Schwartz: Sur l'impossibilité de la multiplication des distributions.C. R. Acad. Sci. Paris 239 (1954), 847-848. Zbl 0056.10602, MR 0064324 |
| . |
