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Compensated compactness and time-periodic solutions to non-autonomous quasilinear telegraph equations

Eduard Feireisl

Aplikace matematiky (1990)

  • Volume: 35, Issue: 3, page 192-208
  • ISSN: 0862-7940

Abstract

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In the present paper, the existence of a weak time-periodic solution to the nonlinear telegraph equation U t t + d U t - σ ( x , t , U x ) x + a U = f ( x , t , U x , U t , U ) with the Dirichlet boundary conditions is proved. No “smallness” assumptions are made concerning the function f . The main idea of the proof relies on the compensated compactness theory.

How to cite

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Feireisl, Eduard. "Compensated compactness and time-periodic solutions to non-autonomous quasilinear telegraph equations." Aplikace matematiky 35.3 (1990): 192-208. <http://eudml.org/doc/15624>.

@article{Feireisl1990,
abstract = {In the present paper, the existence of a weak time-periodic solution to the nonlinear telegraph equation $U_\{tt\}+dU_t-\sigma (x,t,U_x)_x+aU=f(x,t,U_x,U_t,U)$ with the Dirichlet boundary conditions is proved. No “smallness” assumptions are made concerning the function $f$. The main idea of the proof relies on the compensated compactness theory.},
author = {Feireisl, Eduard},
journal = {Aplikace matematiky},
keywords = {telegraph equation; compensated compactness; vanishing viscosity method; nonlinear telegraph equation; compensated compactness theory; vanishing viscosity method},
language = {eng},
number = {3},
pages = {192-208},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Compensated compactness and time-periodic solutions to non-autonomous quasilinear telegraph equations},
url = {http://eudml.org/doc/15624},
volume = {35},
year = {1990},
}

TY - JOUR
AU - Feireisl, Eduard
TI - Compensated compactness and time-periodic solutions to non-autonomous quasilinear telegraph equations
JO - Aplikace matematiky
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 3
SP - 192
EP - 208
AB - In the present paper, the existence of a weak time-periodic solution to the nonlinear telegraph equation $U_{tt}+dU_t-\sigma (x,t,U_x)_x+aU=f(x,t,U_x,U_t,U)$ with the Dirichlet boundary conditions is proved. No “smallness” assumptions are made concerning the function $f$. The main idea of the proof relies on the compensated compactness theory.
LA - eng
KW - telegraph equation; compensated compactness; vanishing viscosity method; nonlinear telegraph equation; compensated compactness theory; vanishing viscosity method
UR - http://eudml.org/doc/15624
ER -

References

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