Global solution to the Cauchy problem of nonlinear thermodiffusion in a solid body

@article{ArkadiuszSzymaniec2010,
abstract = {We consider the initial-value problem for a nonlinear hyperbolic-parabolic system of three coupled partial differential equations of second order describing the process of thermodiffusion in a solid body (in one-dimensional space). We prove global (in time) existence and uniqueness of the solution to the initial-value problem for this nonlinear system. The global existence is proved using time decay estimates for the solution of the associated linearized problem. Next, we prove an energy estimate in Sobolev spaces with constant independent of time. Such an energy estimate allows us to apply the standard continuation argument to continue the local solution to be defined for all times.},
author = {Arkadiusz Szymaniec},
journal = {Applicationes Mathematicae},
keywords = {hyperbolic-parabolic system; energy estimate; continuation argument},
language = {eng},
number = {4},
pages = {437-458},
title = {Global solution to the Cauchy problem of nonlinear thermodiffusion in a solid body},
url = {http://eudml.org/doc/279878},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Arkadiusz Szymaniec
TI - Global solution to the Cauchy problem of nonlinear thermodiffusion in a solid body
JO - Applicationes Mathematicae
PY - 2010
VL - 37
IS - 4
SP - 437
EP - 458
AB - We consider the initial-value problem for a nonlinear hyperbolic-parabolic system of three coupled partial differential equations of second order describing the process of thermodiffusion in a solid body (in one-dimensional space). We prove global (in time) existence and uniqueness of the solution to the initial-value problem for this nonlinear system. The global existence is proved using time decay estimates for the solution of the associated linearized problem. Next, we prove an energy estimate in Sobolev spaces with constant independent of time. Such an energy estimate allows us to apply the standard continuation argument to continue the local solution to be defined for all times.
LA - eng
KW - hyperbolic-parabolic system; energy estimate; continuation argument
UR - http://eudml.org/doc/279878
ER -