Continuous dependence for BV-entropy solutions to strongly degenerate parabolic equations with variable coefficients

Watanabe, Hiroshi

  • Proceedings of Equadiff 14, Publisher: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing(Bratislava), page 315-324

Abstract

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We consider the Cauchy problem for degenerate parabolic equations with variable coefficients. The equation has nonlinear convective term and degenerate diffusion term which depends on the spatial and time variables. In this paper, we prove the continuous dependence for entropy solutions in the space BV to the problem not only initial function but also all coefficients.

How to cite

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Watanabe, Hiroshi. "Continuous dependence for BV-entropy solutions to strongly degenerate parabolic equations with variable coefficients." Proceedings of Equadiff 14. Bratislava: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, 2017. 315-324. <http://eudml.org/doc/294937>.

@inProceedings{Watanabe2017,
abstract = {We consider the Cauchy problem for degenerate parabolic equations with variable coefficients. The equation has nonlinear convective term and degenerate diffusion term which depends on the spatial and time variables. In this paper, we prove the continuous dependence for entropy solutions in the space BV to the problem not only initial function but also all coefficients.},
author = {Watanabe, Hiroshi},
booktitle = {Proceedings of Equadiff 14},
keywords = {Strongly degenerate parabolic, continuous dependence, BV -entropy solution},
location = {Bratislava},
pages = {315-324},
publisher = {Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing},
title = {Continuous dependence for BV-entropy solutions to strongly degenerate parabolic equations with variable coefficients},
url = {http://eudml.org/doc/294937},
year = {2017},
}

TY - CLSWK
AU - Watanabe, Hiroshi
TI - Continuous dependence for BV-entropy solutions to strongly degenerate parabolic equations with variable coefficients
T2 - Proceedings of Equadiff 14
PY - 2017
CY - Bratislava
PB - Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing
SP - 315
EP - 324
AB - We consider the Cauchy problem for degenerate parabolic equations with variable coefficients. The equation has nonlinear convective term and degenerate diffusion term which depends on the spatial and time variables. In this paper, we prove the continuous dependence for entropy solutions in the space BV to the problem not only initial function but also all coefficients.
KW - Strongly degenerate parabolic, continuous dependence, BV -entropy solution
UR - http://eudml.org/doc/294937
ER -

References

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  10. Watanabe, H., Entropy solutions to strongly degenerate parabolic equations with zero-flux boundary conditions, , Adv. Math. Sci. Appl., 23 (2013), no. 1, 209–234. MR3155452
  11. Watanabe, H., Strongly degenerate parabolic equations with variable coefficients, , Adv. Math. Sci. Appl., 26 (2017), 143–173. MR3821859
  12. Watanabe, H., Oharu, S., BV-entropy solutions to strongly degenerate parabolic equations, , Adv. Differential Equations 15(7-8) (2010), 757–800. MR2650587
  13. Watanabe, H., Oharu, S., Finite-difference approximations to a class of strongly degenerate parabolic equations, , Adv. Math. Sci. Appl., 20 (2010), no. 2, 319–347. MR2815744
  14. Ziemer, W. P., Weakly differentiable functions, , Springer-Verlag, New York, (1989). MR1014685

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