Results 41 to 50 of about 72,789 (297)
Self‐Similar Blowup for the Cubic Schrödinger Equation
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We give a rigorous proof for the existence of a finite‐energy, self‐similar solution to the focusing cubic Schrödinger equation in three spatial dimensions. The proof is computer‐assisted and relies on a fixed point argument that shows the existence of a solution in the vicinity of a numerically constructed approximation.
Roland Donninger, Birgit Schörkhuber
wiley +1 more source
Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
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Front Propagation Through a Perforated Wall
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We consider a bistable reaction– diffusion equation ut=Δu+f(u)$u_t=\Delta u +f(u)$ on RN${\mathbb {R}}^N$ in the presence of an obstacle K$K$, which is a wall of infinite span with many holes. More precisely, K$K$ is a closed subset of RN${\mathbb {R}}^N$ with smooth boundary such that its projection onto the x1$x_1$‐axis is bounded and that ...
Henri Berestycki +2 more
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Journal of Function Spaces, 2021 The primary objective of this study is to introduce two novel extragradient-type iterative schemes for solving variational inequality problems in a real Hilbert space.
Chainarong Khunpanuk +2 more
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On the Continuity of the Nemitsky Operator Induced by a Lipschitz Continuous Map [PDF]
Proceedings of the American Mathematical Society, 1991 Let \(f: \mathbb{R}^ N\to\mathbb{R}^ k\) be a Lipschitz continuous function, let \(\Omega\) be a bounded domain in \(\mathbb{R}^ n\),and take ...
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Edge‐Length Preserving Embeddings of Graphs Between Normed Spaces
Journal of Graph Theory, EarlyView.ABSTRACT The concept of graph embeddability, initially formalized by Belk and Connelly and later expanded by Sitharam and Willoughby, extends the question of embedding finite metric spaces into a given normed space. A finite simple graph G = ( V , E ) $G=(V,E)$ is said to be ( X , Y ) $(X,Y)$‐embeddable if any set of induced edge lengths from an ...
Sean Dewar +3 more
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Automatic Continuity of Lipschitz Algebras
Journal of Functional Analysis, 1995 If \(\{A_\alpha\}\) is a parametrized family of Banach algebras, for which ...
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Lipschitz Continuous Algorithms for Graph Problems
2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS), 2023 Graph algorithms are widely used for decision making and knowledge discovery. To ensure their effectiveness, it is essential that their output remains stable even when subjected to small perturbations to the input because frequent output changes can result in costly decisions, reduced user trust, potential security concerns, and lack of replicability ...
Soh Kumabe, Yuichi Yoshida
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A Coarse Geometric Approach to Graph Layout Problems
Journal of Graph Theory, EarlyView.ABSTRACT We define a range of new coarse geometric invariants based on various graph–theoretic measures of complexity for finite graphs, including treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these invariants can be used to define functions which satisfy a strong monotonicity property, namely, they are ...
Wanying Huang +3 more
wiley +1 more source
Abstract and Applied Analysis, 2013 The existence of the exponential attractors for coupled Ginzburg-Landau equations describing Bose-Einstein condensates and nonlinear optical waveguides and cavities with periodic initial boundary is obtained by showing Lipschitz continuity and the ...
Gui Mu, Jun Liu
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