# American Institute of Mathematical Sciences

June  2003, 2(2): 259-275. doi: 10.3934/cpaa.2003.2.259

## Asymptotic shape of a solution for the Plasma problem in higher dimensional spaces

 1 Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan

Received  July 2002 Revised  February 2003 Published  March 2003

We consider asymptotic shape of a solution for a semilinear elliptic equation in dimensions 3 or over, by using singular perturbation technique. The equations arise in the Plasma Problem. The solution is obtained as a global minimizer of some energy functional. Precisely energy estimates and uniqueness of a solution for limiting problem gives information about asymptotic shape of a solution.
Citation: Masataka Shibata. Asymptotic shape of a solution for the Plasma problem in higher dimensional spaces. Communications on Pure & Applied Analysis, 2003, 2 (2) : 259-275. doi: 10.3934/cpaa.2003.2.259
 [1] Christian Lax, Sebastian Walcher. Singular perturbations and scaling. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 1-29. doi: 10.3934/dcdsb.2019170 [2] Zvi Artstein. Invariance principle in the singular perturbations limit. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3653-3666. doi: 10.3934/dcdsb.2018309 [3] Michel Chipot, Senoussi Guesmia. On the asymptotic behavior of elliptic, anisotropic singular perturbations problems. Communications on Pure & Applied Analysis, 2009, 8 (1) : 179-193. doi: 10.3934/cpaa.2009.8.179 [4] Senoussi Guesmia, Abdelmouhcene Sengouga. Some singular perturbations results for semilinear hyperbolic problems. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 567-580. doi: 10.3934/dcdss.2012.5.567 [5] Claudio Marchi. On the convergence of singular perturbations of Hamilton-Jacobi equations. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1363-1377. doi: 10.3934/cpaa.2010.9.1363 [6] Chiara Zanini. Singular perturbations of finite dimensional gradient flows. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 657-675. doi: 10.3934/dcds.2007.18.657 [7] Canela Jordi. Singular perturbations of Blaschke products and connectivity of Fatou components. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 3567-3585. doi: 10.3934/dcds.2017153 [8] Paola Mannucci, Claudio Marchi, Nicoletta Tchou. Asymptotic behaviour for operators of Grushin type: Invariant measure and singular perturbations. Discrete & Continuous Dynamical Systems - S, 2019, 12 (1) : 119-128. doi: 10.3934/dcdss.2019008 [9] Ogabi Chokri. On the $L^p-$ theory of Anisotropic singular perturbations of elliptic problems. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1157-1178. doi: 10.3934/cpaa.2016.15.1157 [10] Youri V. Egorov, Evariste Sanchez-Palencia. Remarks on certain singular perturbations with ill-posed limit in shell theory and elasticity. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1293-1305. doi: 10.3934/dcds.2011.31.1293 [11] Yuzo Hosono. Traveling waves for a diffusive Lotka-Volterra competition model I: singular perturbations. Discrete & Continuous Dynamical Systems - B, 2003, 3 (1) : 79-95. doi: 10.3934/dcdsb.2003.3.79 [12] Said Hadd, Rosanna Manzo, Abdelaziz Rhandi. Unbounded perturbations of the generator domain. Discrete & Continuous Dynamical Systems - A, 2015, 35 (2) : 703-723. doi: 10.3934/dcds.2015.35.703 [13] Michel Duprez, Guillaume Olive. Compact perturbations of controlled systems. Mathematical Control & Related Fields, 2018, 8 (2) : 397-410. doi: 10.3934/mcrf.2018016 [14] Mohamed Sami ElBialy. Locally Lipschitz perturbations of bisemigroups. Communications on Pure & Applied Analysis, 2010, 9 (2) : 327-349. doi: 10.3934/cpaa.2010.9.327 [15] Alfonso Artigue. Lipschitz perturbations of expansive systems. Discrete & Continuous Dynamical Systems - A, 2015, 35 (5) : 1829-1841. doi: 10.3934/dcds.2015.35.1829 [16] Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš. Perturbations of nonlinear eigenvalue problems. Communications on Pure & Applied Analysis, 2019, 18 (3) : 1403-1431. doi: 10.3934/cpaa.2019068 [17] Gianne Derks, Sara Maad, Björn Sandstede. Perturbations of embedded eigenvalues for the bilaplacian on a cylinder. Discrete & Continuous Dynamical Systems - A, 2008, 21 (3) : 801-821. doi: 10.3934/dcds.2008.21.801 [18] Chao Liang, Wenxiang Sun, Jiagang Yang. Some results on perturbations of Lyapunov exponents. Discrete & Continuous Dynamical Systems - A, 2012, 32 (12) : 4287-4305. doi: 10.3934/dcds.2012.32.4287 [19] Claudio Buzzi, Claudio Pessoa, Joan Torregrosa. Piecewise linear perturbations of a linear center. Discrete & Continuous Dynamical Systems - A, 2013, 33 (9) : 3915-3936. doi: 10.3934/dcds.2013.33.3915 [20] Stefanella Boatto. Curvature perturbations and stability of a ring of vortices. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 349-375. doi: 10.3934/dcdsb.2008.10.349

2018 Impact Factor: 0.925