Variational principles for parabolic equations

Aplikace matematiky (1969)

• Volume: 14, Issue: 4, page 278-297
• ISSN: 0862-7940

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Abstract

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New types of variational principles, each of them equivalent to the linear mixed problem for parabolic equation with initial and combined boundary conditions having been suggested by physicists, are discussed. Though the approach used here is purely mathematical so that it makes possible application to all mixed problems of mathematical physics with parabolic equations, only the example of heat conductions is used to show the physical interpretation. The principles under consideration are of two kinds. The first kind presents a variational characterization of the original problem, expressed in terms of a scalar function (temperature). The principles of the second kind characterize the same problem, formulated in terms of other variables, e.g. of a vector function (heat flux or entropy displacements).

How to cite

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Hlaváček, Ivan. "Variational principles for parabolic equations." Aplikace matematiky 14.4 (1969): 278-297. <http://eudml.org/doc/14603>.

@article{Hlaváček1969,
abstract = {New types of variational principles, each of them equivalent to the linear mixed problem for parabolic equation with initial and combined boundary conditions having been suggested by physicists, are discussed. Though the approach used here is purely mathematical so that it makes possible application to all mixed problems of mathematical physics with parabolic equations, only the example of heat conductions is used to show the physical interpretation. The principles under consideration are of two kinds. The first kind presents a variational characterization of the original problem, expressed in terms of a scalar function (temperature). The principles of the second kind characterize the same problem, formulated in terms of other variables, e.g. of a vector function (heat flux or entropy displacements).},
author = {Hlaváček, Ivan},
journal = {Aplikace matematiky},
keywords = {partial differential equations},
language = {eng},
number = {4},
pages = {278-297},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Variational principles for parabolic equations},
url = {http://eudml.org/doc/14603},
volume = {14},
year = {1969},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - Variational principles for parabolic equations
JO - Aplikace matematiky
PY - 1969
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 14
IS - 4
SP - 278
EP - 297
AB - New types of variational principles, each of them equivalent to the linear mixed problem for parabolic equation with initial and combined boundary conditions having been suggested by physicists, are discussed. Though the approach used here is purely mathematical so that it makes possible application to all mixed problems of mathematical physics with parabolic equations, only the example of heat conductions is used to show the physical interpretation. The principles under consideration are of two kinds. The first kind presents a variational characterization of the original problem, expressed in terms of a scalar function (temperature). The principles of the second kind characterize the same problem, formulated in terms of other variables, e.g. of a vector function (heat flux or entropy displacements).
LA - eng
KW - partial differential equations
UR - http://eudml.org/doc/14603
ER -

References

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