DSpace Community: KAIST Dept. of Mathematical Sciences
http://hdl.handle.net/10203/527
KAIST Dept. of Mathematical Sciences2017-08-17T11:16:35ZInviscid traveling waves of monostable nonlinearity
http://hdl.handle.net/10203/224020
Title: Inviscid traveling waves of monostable nonlinearity
Authors: Choi, Sun-Ho; Chung, Jaywan; Kim, Yong-Jung
Abstract: Inviscid traveling waves are ghost-like phenomena that do not appear in reality because of their instability. However, they are the reason for the complexity of the traveling wave theory of reaction diffusion equations and understanding them will help to resolve related puzzles. In this article, we obtain the existence, the uniqueness and the regularity of inviscid traveling waves under a general monostable nonlinearity that includes non-Lipschitz continuous reaction terms. Solution structures are obtained such as the thickness of the tail and the free boundaries. (C) 2017 Elsevier Ltd. All rights reserved.2017-09-01T00:00:00ZLocal universal lifting spaces of mod l Galois representations
http://hdl.handle.net/10203/223404
Title: Local universal lifting spaces of mod l Galois representations
Authors: Choi, Suh Hyun
Abstract: Let p and l be distinct primes, K a finite extension of Q(p), and (rho) over bar : Gal((K) over bar /K)-> GL(n),((F) over barl) a mod l Galois representation. In this paper, we show that the generic fiber of universal lifting space of (rho) over bar is equidimensional of dimension n(2). We also characterize the irreducible components of the generic fiber of the universal lifting space which represent the liftings rho's of (rho) over bar with unipotent rho vertical bar I-K's, when pi', is trivial or n <= 4 and the square of the order of the residue field of K is not equal to 1 mod l. (C) 2017 Elsevier Inc. All rights reserved.2017-07-01T00:00:00ZSymmetry breaking bifurcations for an overdetermined boundary value problem on an exterior domain issued from electrodynamics
http://hdl.handle.net/10203/224859
Title: Symmetry breaking bifurcations for an overdetermined boundary value problem on an exterior domain issued from electrodynamics
Authors: Morabito, Filippo
Abstract: We consider an electrically charged fluid occupying a solid cylindrical region ohm of R-3. Outside the domain ohm there is an electric field with electric potential which solves the Laplace equation and diverges as the distance from the axis tends to infinity. At partial derivative ohm the potential is constant and there is a balance between the pressure difference inside and outside the fluid, capillary forces proportional to the mean curvature and electrostatic repulsion of charges. We are interested in showing the existence of domains different from the solid cylinder ohm and satisfying the conditions described above. This problem is equivalent to an overdetermined elliptic boundary value problem on an exterior domain. We show the bifurcation phenomenon occurs and produces the deformation of the solid cylinder into rippled cylinders. (C) 2017 Elsevier Ltd. All rights reserved.2017-07-01T00:00:00ZTowering Phenomena for the Yamabe Equation on Symmetric Manifolds
http://hdl.handle.net/10203/225092
Title: Towering Phenomena for the Yamabe Equation on Symmetric Manifolds
Authors: Morabito, Filippo; Pistoia, Angela; Vaira, Giusi
Abstract: Let (M, g) be a compact smooth connected Riemannian manifold (without boundary) of dimension N ae<yen> 7. Assume M is symmetric with respect to a point xi (0) with non-vanishing Weyl's tensor. We consider the linear perturbation of the Yamabe problem We prove that for any k a a"center dot, there exists epsilon (k) > 0 such that for all epsilon a (0, epsilon (k) ) the problem (P (oee-) ) has a symmetric solution u (epsilon) , which looks like the superposition of k positive bubbles centered at the point xi (0) as epsilon -> 0. In particular, xi (0) is a towering blow-up point.2017-07-01T00:00:00Z