Temat: general solution - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: A general study of fundamental solutions in aniotropicthermoelastic media with mass diffusion and voids
Autorzy:: Chawla, Vijay
Kamboj, Deepmala
Powiązania:: https://bibliotekanauki.pl/articles/1839675.pdf
Data publikacji:: 2020
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:: termosprężystość
dyfuzja masy
źródło ciepła
general solution
fundamental solution
thermoelastic
voids
mass diffusion
Opis:: The present paper deals with the study of a fundamental solution in transversely isotropic thermoelastic media with mass diffusion and voids. For this purpose, a two-dimensional general solution in transversely isotropic thermoelastic media with mass diffusion and voids is derived first. On the basis of the obtained general solution, the fundamental solution for a steady point heat source on the surface of a semi-infinite transversely isotropic thermoelastic material with mass diffusion and voids is derived by nine newly introduced harmonic functions. The components of displacement, stress, temperature distribution, mass concentration and voids are expressed in terms of elementary functions and are convenient to use. From the present investigation, some special cases of interest are also deduced and compared with the previous results obtained, which prove the correctness of the present result.
Źródło:: International Journal of Applied Mechanics and Engineering; 2020, 25, 4; 22-41
1734-4492
2353-9003
Pojawia się w:: International Journal of Applied Mechanics and Engineering
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Sur la méthode de l’intégrale particulière et sur ses conséquences pour l’équation de Riccati et pour les équations différentielles linéaires et homogènes d’ordre supérieur
Autorzy:: Kapcia, Andrzej
Powiązania:: https://bibliotekanauki.pl/articles/744820.pdf
Data publikacji:: 2007
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: differential equation
linear
homogenous
order
particular solution
superclass
subclass
inverse operator
linearly independent
effective integrability
general solution
Opis:: This paper presents the method of particular solution for solving the Riccati equation and linear homogenous equations of second and third order, as well as its certain application to linear homogenous equations of n-th order. The conditions of effective integrability for equations (0.1) and (0.2) are expressed in symbolic (operator) form and also for equation (0.3) in fully expanded form. There have been proved three theorems which state the following: for any subclass of differential equations of the form (0.1), (0.2), (0.3), if there are known, respectively: a particular solution \(y_0\), a particular solution u 0 , two linearly independent particular solutions \(u_1 , u_2\), then it is possible to construct superclasses of differential equations of the given class, using classes cited in [6, 7, 8, 9]. Moreover, one may obtain their effectively integrable generalizations. Numerous examples provided illustrate the above results. The article presents also a practical way of applying the method of particular solution to linear equations of n-th order. This method enables us to integrate more general equations than those described in [4, 5, 14] of the form (0.1), (0.2), (0.3), (0.4) for which the particular solutions are cited therein.
Źródło:: Commentationes Mathematicae; 2007, 47, 2
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

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