Blow-up on metric graphs and Riemannian manifolds
نویسندگان
چکیده
We study blow-up versus global existence of solutions to a model semilinear parabolic equation in metric measure spaces. Applications graphs and Riemannian manifolds are considered, pointing out the occurrence Fujita phenomenon.
منابع مشابه
Blow-up Solutions for Asymptotically Critical Elliptic Equations on Riemannian Manifolds
Given (M, g) a smooth, compact Riemannian n-manifold, we consider equations like ∆gu + hu = u −1−ε, where h is a C-function on M , the exponent 2∗ = 2n/ (n− 2) is critical from the Sobolev viewpoint, and ε is a small real parameter such that ε→ 0. We prove the existence of blowing-up families of positive solutions in the subcritical and supercritical case when the graph of h is distinct at some...
متن کاملMetric transformations under collapsing of Riemannian manifolds
Gromov-Hausdorff convergence is an important tool in comparison Riemannian geometry. Given a sequence of Riemannian manifolds of dimension n with Ricci curvature bounded from below, Gromov’s precompactness theorem says that a subsequence will converge in the pointed Gromov-Hausdorff topology to a length space [G-99, Section 5A]. If the sequence has bounded sectional curvature, then the limit wi...
متن کاملHigher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs
5 Analysis on weighted graphs 23 5.1 Measures on graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 5.2 Discrete Laplacian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.3 Green’s formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.4 Integration versus Summation . . . . . . . . . . . . . . . . . . . . . . ...
متن کاملBlow-up Results for Nonlinear Parabolic Equations on Manifolds
1. Introduction. The aim of this paper is threefold. First, by a unified approach, we prove that several classical blow-up results obtained over the last three decades for semilinear and quasilinear parabolic problems in R n are valid on noncompact, complete Riemannian manifolds, which include those with nonnegative Ricci curvatures. Next, we remove some unnecessary a priori growth conditions o...
متن کاملA Geometry Preserving Kernel over Riemannian Manifolds
Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems-series B
سال: 2023
ISSN: ['1531-3492', '1553-524X']
DOI: https://doi.org/10.3934/dcdsb.2023016