A Boundary Value Problem Connected with Response of Semi-space to a Short Laser Pulse

Gaetano Fichera

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1997)

  • Volume: 8, Issue: 3, page 197-228
  • ISSN: 1120-6330

Abstract

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In this paper a mixed boundary value problem for the fourth order hyperbolic equation with constant coefficients which is connected with response of semi-space to a short laser pulse» and belongs to generalized Thermoelasticity is studied. This problem was considered by R. B. Hetnarski and J. Ignaczak, who established some important physical consequences. The present paper contains proof of the existence, uniqueness and continuous dependence of a solution on the datum, together with an effective method for numerical computation of a solution and the behaviour of solutions as t → ∞

How to cite

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Fichera, Gaetano. "A Boundary Value Problem Connected with Response of Semi-space to a Short Laser Pulse." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 8.3 (1997): 197-228. <http://eudml.org/doc/244317>.

@article{Fichera1997,
abstract = {In this paper a mixed boundary value problem for the fourth order hyperbolic equation with constant coefficients which is connected with response of semi-space to a short laser pulse» and belongs to generalized Thermoelasticity is studied. This problem was considered by R. B. Hetnarski and J. Ignaczak, who established some important physical consequences. The present paper contains proof of the existence, uniqueness and continuous dependence of a solution on the datum, together with an effective method for numerical computation of a solution and the behaviour of solutions as \( t \rightarrow \infty \)},
author = {Fichera, Gaetano},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Hyperbolic equations; Mixed boundary value problems; Tauber-type theorem; Asymptotics of solutions for large values of the time; fourth order hyperbolic equation},
language = {eng},
month = {10},
number = {3},
pages = {197-228},
publisher = {Accademia Nazionale dei Lincei},
title = {A Boundary Value Problem Connected with Response of Semi-space to a Short Laser Pulse},
url = {http://eudml.org/doc/244317},
volume = {8},
year = {1997},
}

TY - JOUR
AU - Fichera, Gaetano
TI - A Boundary Value Problem Connected with Response of Semi-space to a Short Laser Pulse
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1997/10//
PB - Accademia Nazionale dei Lincei
VL - 8
IS - 3
SP - 197
EP - 228
AB - In this paper a mixed boundary value problem for the fourth order hyperbolic equation with constant coefficients which is connected with response of semi-space to a short laser pulse» and belongs to generalized Thermoelasticity is studied. This problem was considered by R. B. Hetnarski and J. Ignaczak, who established some important physical consequences. The present paper contains proof of the existence, uniqueness and continuous dependence of a solution on the datum, together with an effective method for numerical computation of a solution and the behaviour of solutions as \( t \rightarrow \infty \)
LA - eng
KW - Hyperbolic equations; Mixed boundary value problems; Tauber-type theorem; Asymptotics of solutions for large values of the time; fourth order hyperbolic equation
UR - http://eudml.org/doc/244317
ER -

References

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  1. HETNARSKI, R. B. - IGNACZAK, J., Generalized thermoelasticity: closed form solution. Journal of Thermal Stresses, v. 16, n. 4, 1993, 473-498. MR1245181DOI10.1080/01495739308946241
  2. HETNARSKI, R. B. - IGNACZAK, J., Generalized thermoelasticity: response of semispace to a short laser pulse. Journal of Thermal Stresses, v. 17, 1994, 377-396. MR1289595DOI10.1080/01495739408946267
  3. AGMON, S., Problème mixte pour les équations hyperboliques d'ordre supérieur. Colloq. Intern. Equations aux dérivées partielles. CNRS, Paris1962, 1-6. Zbl0231.35053
  4. SAKAMOTO, R., Mixed problems for hyperbolic equations, I, II. J. Math. Kyoto University, 10:3, 1970, 349-373,403-417. Zbl0203.10001
  5. SAKAMOTO, R., On a class of hyperbolic mixed problems. J. Math. Kyoto University, 16:2, 1976, 429-474. Zbl0345.35067MR422891
  6. IVRII, V. YA. - VOLEVICH, L. R., Hyperbolic equations. In: I. G. Petrovsky selected works. Part. I. Gordon and Breach Publ., 1996, 410-442. 
  7. DOETSCH, G., Handbuch der Laplace-Transformation. Band I. Théorie der Laplace Transformation. Verlag Birkhäuser, Basel1950. Zbl0070.33102MR344808
  8. PETROVSKY, G., Lectures on Partial Differential Equations. Interscience Publishers Inc., New York1954. Zbl0059.08402MR65760

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