Existence of solutions to an initial Dirichlet problem of evolutional -Laplace equations
Songzhe Lian
Institute of Mathematics, Jilin University, Changchun, Jilin 130012, Peopleʼs Republic of ChinaWenjie Gao
Institute of Mathematics, Jilin University, Changchun, Jilin 130012, Peopleʼs Republic of ChinaHongjun Yuan
Institute of Mathematics, Jilin University, Changchun, Jilin 130012, Peopleʼs Republic of ChinaChunling Cao
Institute of Mathematics, Jilin University, Changchun, Jilin 130012, Peopleʼs Republic of China
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Abstract
The existence and uniqueness of weak solutions are studied to the initial Dirichlet problem of the equation
with . The problems describe the motion of generalized Newtonian fluids which were studied by some other authors in which the exponent was required to satisfy a logarithmic Hölder continuity condition. The authors in this paper use a difference scheme to transform the parabolic problem to a sequence of elliptic problems and then obtain the existence of solutions with less constraint to . The uniqueness is also proved.
Cite this article
Songzhe Lian, Wenjie Gao, Hongjun Yuan, Chunling Cao, Existence of solutions to an initial Dirichlet problem of evolutional -Laplace equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012), no. 3, pp. 377–399
DOI 10.1016/J.ANIHPC.2012.01.001