Thermal Waves, Second Sound. Works of Witold Kosiński

• Autorzy: Saxton K. , Saxton R.

Identyfikatory

DOI

10.14708/ma.v43i2.648

Warianty tytułu

PL

Fale termiczne, Drugi dźwiek. Wyniki prac Witolda Kosińskiego

• Języki publikacji: EN

Abstrakty

EN

This paper is dedicated to Witold Kosiński. Our contribution to this special issue will concentrate on the properties of thermal waves, one of many scientific interests of our friend and collaborator, and this article is dedicated to his memory. Working together with Witold was always an insightful and pleasant experience, and it benefited all of his coworkers including the authors of this note. His scope of research was broad, spanning many disciplines and applications. Here we focus on a few of those aspects to which he applied a deep knowledge of continuum thermodynamics and its mathematical foundations.

PL

Niniejsza praca jest poświęcona pamięci naszego przyjaciela Witolda Kosińskego. Chcielibyśmy przedstawić jego najważniejsze osiągnięcia w dziedzinie propagacji fal termicznych, termodynamiki i teorii hiperbolicznych układów różniczkowych. Zakres badań Kosińskiego był bardzo bogaty. Obejmował wiele dyscyplin na pograniczu mechaniki, matematyki i teorii komputerowych. Współpraca z Witoldem była owocna, zawsze wypełniona entuzjazmem i wzajemnym szacunkiem. Autorzy tego artykułu jak i inni współpracownicy Witolda korzystali z jego wiedzy i zawodowego doświadczenia. Bedzie nam go bardzo brakowało.

Słowa kluczowe

EN

continuum thermodynamics; nonlinear waves; singularities; conservation laws

PL

mechanika ośrodków ciągłych; fale nieliniowe; osobliwości; prawa zachowania

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2015
• Tom: Vol. 43, No. 2
• Strony: 291--303
• Opis fizyczny: Bibliogr. 25 poz., fot.

Twórcy

autor

Saxton K.

• Loyola University, Department of Mathematical Sciences, New Orleans, LA 70118, U.S.A.

autor

Saxton R.

• University of New Orleans, Department of Mathematics, New Orleans, LA 70148, U.S.A.

Bibliografia

• [1] M. Arcisz and W. Kosiński, Hugoniot relations and heat conduction laws, J. Thermal Stresses 19 (1996), no. 1, 17–38.
• [2] V. Antonio Cimmelli and Witold Kosiński, Superfluidity and internal parameters in helium II, Waves and stability in continuous media (Bologna, 1993) (S. Rionero and T. Ruggeri, eds.), Ser. Adv. Math. Appl. Sci., vol. 23, World Sci. Publ., River Edge, NJ, 1994, pp. 76–81. MR 1320066
• [3] Vito Antonio Cimmelli and Witold Kosiński, Nonequilibrium semi–empirical temperature in materials with thermal relaxation, Arch. Mech. 43 (1991), no. 6, 753–767.
• [4] W. Kosiński and W. Wojno, Evolution hyperbolic equations for heat conduction, Thermodynamics and kinetic theory. V Polish-Italian Meeting on Thermodynamics and Kinetic Theory, Madralin 1990, Ser. Adv. Math. Appl. Sci., vol. 12, World Sci. Publ., River Edge, NJ, 1992, pp. 11–22. MR 1170162 (93d:73007)
• [5] W. Kosiński and W. Wojno, Well posedness results for a nonlinear hyperbolic heat equation, Ricerche Mat. 42 (1993), no. 1, 49–68. MR 1283805 (95h:35138)
• [6] Vito Antonio Cimmelli, Witold Kosiński, and Katarzyna Saxton, Modified fourier law, comparison of two approaches, Arch. Mech. 44 (1992), no. 4, 409–415.
• [7] W. Domański, T.F. Jabłoński, and W. Kosiński, Symmetrization of a heat conduction model for a rigid medium., Arch. Mech. 48 (1996), no. 3, 541–550 (English), Zbl 0857.73010.
• [8] W. Domański and W. Kosiński, Asymptotic equations of geometrical optics for two models of hyperbolic heat waves, Arch. Mech. (Arch. Mech. Stos.) 47 (1995), no. 4, 745–753. MR 1364703 (96h:35180)
• [9] K. Frischmuth and W. Kosiński, Thermomechanical coupled waves in a viscoplastic medium, Arch. Mech. (Arch. Mech. Stos.) 54 (2002), no. 5-6, 439–457. MR 1964399 (2004b:74048)
• [10] W. Kosiński, Thermal waves in inelastic bodies, Arch. Mech. (Arch. Mech. Stos.) 27 (1975), no. 5-6, 733–748, MR 0418664. MR 0418664 (54 #6702)
• [11] W. Kosiński, Hyperbolic framework for thermoelastic materials., Arch. Mech. 50 (1998), no. 3, 423–450 (English), Zbl 0949.74005.
• [12] W. Kosiński and K. Saxton, Weak discontinuity waves in materials with semiempirical temperature scale, Arch. Mech. (Arch. Mech. Stos.) 43 (1991), no. 4, 547–559 (1992), MR 1161935. MR 1161935 (92m:80009)
• [13] W. Kosiński, The effect on finite time breakdown due to modified Fourier laws, Quart. Appl. Math. 51 (1993), no. 1, 55–68. MR 1205936 (93m:35118)
• [14] W. Kosiński and W. Wojno, Remarks on internal variable and history descriptions of material, Arch. Mech. (Arch. Mech. Stos.) 25 (1973), 709–713, MR 0368545. MR 0368545 (51 #4786)
• [15] W. Domański, T.J. Jabłoński and W. Kosiński, Gradient generalization to internal state variable approach, Arch. Mech. (Arch. Mech. Stos.) 47 (1995), no. 3, 523–536. MR 1364476 (96k:73015)
• [16] Witold Kosiński, Gradient catastrophe in the solution of nonconservative hyperbolic systems, J. Math. Anal. Appl. 61 (1977), no. 3, 672–688, MR 0460912. MR 0460912 (57 #903)
• [17] Witold Kosiński, Admissibility and uniqueness of weak solutions to hyperbolic systems of balance laws, Math. Methods Appl. Sci. 11 (1989), no. 2, 253–269, MR 984056, doi: 10.1002/mma.1670110206. MR 984056 (90i:35064)
• [18] V. A. Cimmelli, W. Kosiński and K. Saxton, Elastic waves in the presence of a new temperature scale, Elastic Wave Propagation, IUTAM-IUPAP Symposium (1988) (M. F. McCarthy and M. Hayes, eds.), Series in Applied Mathematics and Mechanics, vol. 35, North-Holland, 1989, pp. 629–634.
• [19] M. Arcisz and W. Kosiński, Thermodynamics, admissibility and uniqueness of weak solutions to system of balance laws, Proc. III Meeting on Waves and Stability in Continuous Media, Bari, 7-12 Ottobre 1985 (M. Maiellaro and L. Palese, eds.), 1989, pp. 205–245.
• [20] Witold Kosiński, Thermal waves in the kinematic theory, Proc. IUTAM Symp. Nonlinear Waves in Solids, Victoria, B. C., Canada, Aug. 15-20, 1993. (Fairfield, New Jersey), ASME Book No. Appl. Mech. Rev., vol. 137, ASME, 1994, pp. 247–252. MR 1320066
• [21] V. A. Cimmelli and W. Kosiński, Thermodynamics of continua with heat waves, Thermoelastic Problems and Thermodynamics of Continua, Proc. of the 1995 Joint ASME Applied Mechanics and Materials Summer Meeting, Los Angeles, California, June 28-30,1995, UCLA (L. Brock, ed.), AMD, vol. 198, American Society of Mechanical Engineers, New York, N. Y., 1995, pp. 19–25.
• [22] Witold Kosiński and Kurt Frischmuth, Thermomechanical coupled waves in a nonlinear medium., Wave Motion 34 (2001), no. 1, 131–141 (English), Zbl 1163.74385.
• [23] Witold Kosiński and WłodzimierzWojno, On parabolic regularization of hyperbolic heat conductivity in rigid body., Mech. Teor. Stosow. 34 (1996), no. 1, 67–76 (English), Zbl 0854.73005.
• [24] T. Ruggeri, A. Muracchini, and L. Seccia, Shock waves and second sound in a rigid heat conductor: A critical temperature for naf and bi, Phys. Rev. Lett. 64 (1990), no. 3, 2640–2643, doi: 10.1103/PhysRevLett.64.2640.
• [25] K. Saxton, R. Saxton, and W. Kosiński, On second sound at the critical temperature, Quart. Appl. Math. 57 (1999), no. 4, 723–740. MR 1724302 (2000h:35158)