Complicated Self-Similar Blow-up, Compacton, and Standing Wave Patterns for Four Nonlinear PDEs: a Unified Variational Approach to Elliptic Equations

2014 ◽  
pp. 1-102
Keyword(s):  
Standing Wave ◽  
Elliptic Equations ◽  
Variational Approach ◽  
Blow Up ◽  
Nonlinear Pdes ◽  
Wave Patterns ◽  
Self Similar

scholarly journals Supercritical Elliptic Equations

2012 ◽  
Vol 12 (4) ◽  
Author(s):  
Melanie Rupflin ◽  
Michael Struwe
Keyword(s):  
Elliptic Equations ◽  
Model Equation ◽  
Blow Up ◽  
Radial Solutions ◽  
Elliptic Model ◽  
Self Similar

AbstractFor an elliptic model equation with supercritical power non-linearity we give a complete description of radial solutions and discuss self-similar blow-up solutions.

scholarly journals Blow-up rate and uniqueness of singular radial solutions for a class of quasi-linear elliptic equations

2012 ◽  
Vol 252 (2) ◽  
pp. 1776-1788 ◽  
Author(s):  
Zhifu Xie ◽  
Chunshan Zhao
Keyword(s):  
Elliptic Equations ◽  
Blow Up ◽  
Radial Solutions ◽  
Blow Up Rate

Multiple boundary blow-up solutions for nonlinear elliptic equations

2003 ◽  
Vol 133 (2) ◽  
pp. 225-235 ◽  
Author(s):  
Amandine Aftalion ◽  
Manuel del Pino ◽  
René Letelier
Keyword(s):  
Elliptic Equations ◽  
Blow Up ◽  
A Priori ◽  
Nonlinear Elliptic Equations ◽  
Positive Parameter ◽  
Number Of Solutions ◽  
Bounded Smooth Domain ◽  
Nonlinear Elliptic ◽  
Bounded Smooth

We consider the problem Δu = λf(u) in Ω, u(x) tends to +∞ as x approaches ∂Ω. Here, Ω is a bounded smooth domain in RN, N ≥ 1 and λ is a positive parameter. In this paper, we are interested in analysing the role of the sign changes of the function f in the number of solutions of this problem. As a consequence of our main result, we find that if Ω is star-shaped and f behaves like f(u) = u(u−a)(u−1) with ½ < a < 1, then there is a solution bigger than 1 for all λ and there exists λ0 > 0 such that, for λ < λ0, there is no positive solution that crosses 1 and, for λ > λ0, at least two solutions that cross 1. The proof is based on a priori estimates, the construction of barriers and topological-degree arguments.

Blow-up solutions for asymptotically critical elliptic equations on Riemannian manifolds

2009 ◽  
Vol 58 (4) ◽  
pp. 1719-1746 ◽  
Author(s):  
Anna Maria Micheletti ◽  
Angela Pistoia ◽  
Jerome Vetois
Keyword(s):  
Riemannian Manifolds ◽  
Elliptic Equations ◽  
Blow Up

scholarly journals Development of singularities of the Skyrme model

2020 ◽  
Vol 17 (01) ◽  
pp. 61-73
Author(s):  
Michael McNulty
Keyword(s):  
Sigma Model ◽  
Blow Up ◽  
Strong Field ◽  
Skyrme Model ◽  
Nonlinear Sigma Model ◽  
Field Limit ◽  
Wave Maps ◽  
Self Similar ◽  
Similar Solutions ◽  
Strong Field Limit

The Skyrme model is a geometric field theory and a quasilinear modification of the Nonlinear Sigma Model (Wave Maps). In this paper, we study the development of singularities for the equivariant Skyrme Model, in the strong-field limit, where the restoration of scale invariance allows us to look for self-similar blow-up behavior. After introducing the Skyrme Model and reviewing what’s known about formation of singularities in equivariant Wave Maps, we prove the existence of smooth self-similar solutions to the [Formula: see text]-dimensional Skyrme Model in the strong-field limit, and use that to conclude that the solution to the corresponding Cauchy problem blows-up in finite time, starting from a particular class of everywhere smooth initial data.

scholarly journals Examples of non connective C *-algebras

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Anna Gąsior ◽  
Andrzej Szczepański
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Blow Up ◽  
Fractional Diffusion ◽  
Uniqueness Of Solutions ◽  
C Algebras ◽  
Space Fractional Diffusion Equation ◽  
Self Similar ◽  
Similar Solutions

Abstract This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder’s and Banach’s fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.

Sign in / Sign up

Export Citation Format

Share Document