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

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

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topFichera, 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

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

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