Application of Rothe's method to a parabolic inverse problem with nonlocal boundary condition

Yong-Hyok Jo; Myong-Hwan Ri

Applications of Mathematics (2022)

  • Volume: 67, Issue: 5, page 573-592
  • ISSN: 0862-7940

Abstract

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We consider an inverse problem for the determination of a purely time-dependent source in a semilinear parabolic equation with a nonlocal boundary condition. An approximation scheme for the solution together with the well-posedness of the problem with the initial value u 0 ∈ H 1 ( Ω ) is presented by means of the Rothe time-discretization method. Further approximation scheme via Rothe’s method is constructed for the problem when u 0 ∈ L 2 ( Ω ) and the integral kernel in the nonlocal boundary condition is symmetric.

How to cite

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Jo, Yong-Hyok, and Ri, Myong-Hwan. "Application of Rothe's method to a parabolic inverse problem with nonlocal boundary condition." Applications of Mathematics 67.5 (2022): 573-592. <http://eudml.org/doc/298485>.

@article{Jo2022,
abstract = {We consider an inverse problem for the determination of a purely time-dependent source in a semilinear parabolic equation with a nonlocal boundary condition. An approximation scheme for the solution together with the well-posedness of the problem with the initial value $u_0\in H^1(\Omega )$ is presented by means of the Rothe time-discretization method. Further approximation scheme via Rothe’s method is constructed for the problem when $u_0\in L^2(\Omega )$ and the integral kernel in the nonlocal boundary condition is symmetric.},
author = {Jo, Yong-Hyok, Ri, Myong-Hwan},
journal = {Applications of Mathematics},
keywords = {Rothe's method; nonlocal boundary condition; semilinear parabolic equation; inverse source problem},
language = {eng},
number = {5},
pages = {573-592},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Application of Rothe's method to a parabolic inverse problem with nonlocal boundary condition},
url = {http://eudml.org/doc/298485},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Jo, Yong-Hyok
AU - Ri, Myong-Hwan
TI - Application of Rothe's method to a parabolic inverse problem with nonlocal boundary condition
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 5
SP - 573
EP - 592
AB - We consider an inverse problem for the determination of a purely time-dependent source in a semilinear parabolic equation with a nonlocal boundary condition. An approximation scheme for the solution together with the well-posedness of the problem with the initial value $u_0\in H^1(\Omega )$ is presented by means of the Rothe time-discretization method. Further approximation scheme via Rothe’s method is constructed for the problem when $u_0\in L^2(\Omega )$ and the integral kernel in the nonlocal boundary condition is symmetric.
LA - eng
KW - Rothe's method; nonlocal boundary condition; semilinear parabolic equation; inverse source problem
UR - http://eudml.org/doc/298485
ER -

References

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