An evolutionary weighted $p$-Laplacian with Neumann boundary value condition in a perforated domain
Authors:
Yuanyuan Ke, Jingxue Yin and Chunhua Jin
Journal:
Quart. Appl. Math. 66 (2008), 325-350
MSC (2000):
Primary 35D05, 35B05, 35B45, 35B40
DOI:
https://doi.org/10.1090/S0033-569X-08-01106-7
Published electronically:
March 12, 2008
MathSciNet review:
2416776
Full-text PDF Free Access
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Additional Information
Abstract: In this paper, we study an evolutionary weighted $p$-Laplacian with Neumann boundary value condition in a perforated domain. We discuss the removability of the orifice for the radially symmetric steady solution, the general steady solution and for the evolutionary solution of the problem considered.
References
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References
- E. Dibenedetto, U. Gianazza and V. Vespri, Intrinsic Harnack estimates for nonnegative local solutions of degenerate parabolic equations, Electron. Res. Announc. Amer. Math. Soc., 12(2006), 95–99 (electronic). MR 2237273 (2007d:35163)
- D. Andreucci, P. Bisegna and E. DiBenedetto, Homogenization and concentrated capacity for the heat equation with non-linear variational data in reticular almost disconnected structures and applications to visual transduction, Ann. Mat. Pura Appl. (4), 182(4)(2003), 375–407. MR 2023645 (2004m:35015)
- Ya Zhe Chen and E. DiBenedetto, Hölder estimates of solutions of singular parabolic equations with measurable coefficients, Arch. Rational Mech. Anal., 118(3)(1992), 257–271. MR 1158938 (93a:35092)
- Kazuo Kobayasi, A kinetic approach to comparison properties for degenerate parabolic-hyperbolic equations with boundary conditions, J. Differential Equations, 230(2)(2006), 682–701. MR 2269939
- Tsung-fang Wu, Three positive solutions for nonlinear elliptic equations in finite strip with hole, J. Math. Anal. Appl. 299(1)(2004), 285–299. MR 2091289 (2005h:35108)
- G. Dal Maso and I. V. Skrypnik, A monotonicity approach to nonlinear Dirichlet problems in perforated domains, Adv. Math. Sci. Appl., 11(2)(2001), 721–751. MR 1907464 (2003e:35022)
- A. K. Nandakumaran and M. Rajesh, Homogenization of a parabolic equation in perforated domain with Dirichlet boundary condition, Proc. Indian Acad. Sci. Math. Sci., 112(3)(2002), 425–439. MR 1921791 (2003i:35021)
- M. Rajesh, Convergence of some energies for the Dirichlet problem in perforated domains, Rend. Mat. Appl. (7), 21(1-4)(2001), 259–274. MR 1884947 (2002k:35033)
- Viět Hà Hoàng, Singularly perturbed Dirichlet problems in randomly perforated domains, Comm. Partial Differential Equations, 25(1-2)(2000), 355–375. MR 1737552 (2001g:35022)
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Additional Information
Yuanyuan Ke
Affiliation:
Department of Mathematics, Jilin University, Changchun, Jilin 130012, People’s Republic of China;
School of Mathematics $\&$ Computational Science, Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
Email:
keyy@jlu.edu.cn
Jingxue Yin
Affiliation:
Department of Mathematics, Jilin University, Changchun, Jilin 130012, People’s Republic of China
Email:
yjx@jlu.edu.cn
Chunhua Jin
Affiliation:
Department of Mathematics, Jilin University, Changchun, Jilin 130012, People’s Republic of China
Email:
jinchhua@126.com
Keywords:
Evolutionary weighted $p$-Laplacian,
perforated domain,
orifice
Received by editor(s):
July 13, 2006
Published electronically:
March 12, 2008
Additional Notes:
This work is partially supported by NNSF of China, partially supported by NSFGD-06300481, partially supported by a Specific Foundation for Ph.D. Specialities of Educational Department of China, and partially supported by 985 Projects
Corresponding author. email: jinchhua@126.com
Article copyright:
© Copyright 2008
Brown University
The copyright for this article reverts to public domain 28 years after publication.
