We study a nonlinear fourth-order extension of Richards' equation that describes infiltration processes in unsaturated soils. We prove the well-posedness of the fourth-order equation by first applying Kirchhoff's transformation to linearize the higher-order terms. The transformed equation is then discretized in time and space and a set of a priori estimates is established. These allow, by means of compactness theorems, extracting a unique weak solution. Finally, we use the inverse of Kirchhoff's transformation to prove the well-posedness of the original equation.
%0 Journal Article
%1 ARMITIJUBER2020124005
%A Armiti-Juber, Alaa
%A Rohde, Christian
%D 2020
%J J. Math. Anal. Appl.
%K Existence Kirchhoff's Nonlinear Richards' Uniqueness Weak equation extension fourth-order from:sylviazur ians imported solutions transformation vorlaeufig
%N 2
%P 124005
%R https://doi.org/10.1016/j.jmaa.2020.124005
%T On the well-posedness of a nonlinear fourth-order extension of Richards' equation
%U http://www.sciencedirect.com/science/article/pii/S0022247X20301670
%V 487
%X We study a nonlinear fourth-order extension of Richards' equation that describes infiltration processes in unsaturated soils. We prove the well-posedness of the fourth-order equation by first applying Kirchhoff's transformation to linearize the higher-order terms. The transformed equation is then discretized in time and space and a set of a priori estimates is established. These allow, by means of compactness theorems, extracting a unique weak solution. Finally, we use the inverse of Kirchhoff's transformation to prove the well-posedness of the original equation.
@article{ARMITIJUBER2020124005,
abstract = {We study a nonlinear fourth-order extension of Richards' equation that describes infiltration processes in unsaturated soils. We prove the well-posedness of the fourth-order equation by first applying Kirchhoff's transformation to linearize the higher-order terms. The transformed equation is then discretized in time and space and a set of a priori estimates is established. These allow, by means of compactness theorems, extracting a unique weak solution. Finally, we use the inverse of Kirchhoff's transformation to prove the well-posedness of the original equation.},
added-at = {2020-02-06T09:42:00.000+0100},
author = {Armiti-Juber, Alaa and Rohde, Christian},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/21b495e614f046bff7db4046a2bca1020/mathematik},
doi = {https://doi.org/10.1016/j.jmaa.2020.124005},
interhash = {6c7122c0345159ccbc7d34669adbe6ee},
intrahash = {1b495e614f046bff7db4046a2bca1020},
issn = {0022-247X},
journal = {J. Math. Anal. Appl.},
keywords = {Existence Kirchhoff's Nonlinear Richards' Uniqueness Weak equation extension fourth-order from:sylviazur ians imported solutions transformation vorlaeufig},
number = 2,
pages = 124005,
timestamp = {2020-04-03T08:41:23.000+0200},
title = {On the well-posedness of a nonlinear fourth-order extension of Richards' equation},
url = {http://www.sciencedirect.com/science/article/pii/S0022247X20301670},
volume = 487,
year = 2020
}
