On the Monotone Solutions of Some ODEs. II: Dead-core, Compact-support, and Blow-up Solutions

2006 ◽  
pp. 279-288
Author(s):  
Tadie
Keyword(s):  
Compact Support ◽  
Blow Up ◽  
Dead Core ◽  
Monotone Solutions

The equation utt − Δu = |u|p for the critical value of p

1985 ◽  
Vol 101 (1-2) ◽  
pp. 31-44 ◽  
Author(s):  
Jack Schaeffer
Keyword(s):  
Compact Support ◽  
Finite Time ◽  
Blow Up ◽  
Critical Value ◽  
Cauchy Data ◽  
Three Dimensions ◽  
Dimensional Case ◽  
Small Data ◽  
Two Dimensional ◽  
Three Space

SynopsisThe equation utt − Δu = |u|p is considered in two and three space dimensions. Smooth Cauchy data of compact support are given at t = 0. For the case of three space dimensions, John has shown that solutions with sufficiently small data exist globally in time if but that small data solutions blow up in finite time if Glassey has shown the two dimensional case is similar. This paper shows that small data solutions blow up in finite time when p is the critical value, in three dimensions and in two.

scholarly journals PRO CDH-DESCENT FOR CYCLIC HOMOLOGY AND -THEORY

2014 ◽  
Vol 15 (3) ◽  
pp. 539-567 ◽  
Author(s):  
Matthew Morrow
Keyword(s):  
Compact Support ◽  
Blow Up ◽  
Cyclic Homology ◽  
Finite Characteristic ◽  
Topological Cyclic Homology

In this paper, we prove that cyclic homology, topological cyclic homology, and algebraic $K$-theory satisfy a pro Mayer–Vietoris property with respect to abstract blow-up squares of varieties, in both zero and finite characteristic. This may be interpreted as the well-definedness of $K$-theory with compact support.

Positive solutions for a quasilinear system Via blow up

1993 ◽  
Vol 18 (12) ◽  
pp. 2071-2106
Author(s):  
Philippe Clément ◽  
Raúl Manásevich ◽  
Enzo Mitidieri
Keyword(s):  
Positive Solutions ◽  
Blow Up ◽  
Quasilinear System

: The Blow-Up . Michelangelo Antonioni .

1967 ◽  
Vol 20 (3) ◽  
pp. 28-31
Author(s):  
Max Kozloff
Keyword(s):  
Blow Up ◽  
Michelangelo Antonioni

Gluing Solutions

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Stress Tensor ◽  
Compact Support ◽  
Smooth Solution ◽  
Continuous Solution ◽  
Total Momentum ◽  
Frame Of Reference ◽  
Galilean Transformation ◽  
Hölder Continuous ◽  
Pressure Form ◽  
Original Frame

This chapter deals with the gluing of solutions and the relevant theorem (Theorem 12.1), which states the condition for a Hölder continuous solution to exist. By taking a Galilean transformation if necessary, the solution can be assumed to have zero total momentum. The cut off velocity and pressure form a smooth solution to the Euler-Reynolds equations with compact support when coupled to a smooth stress tensor. The proof of Theorem (12.1) proceeds by iterating Lemma (10.1) just as in the proof of Theorem (10.1). Applying another Galilean transformation to return to the original frame of reference, the theorem is obtained.

Instability and Collapse in Discrete Wave Equations

2005 ◽  
Vol 5 (3) ◽  
pp. 223-241
Author(s):  
A. Carpio ◽  
G. Duro
Keyword(s):  
Continuum Limit ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Blow Up ◽  
Theoretical Predictions ◽  
Initial States ◽  
The Impact ◽  
The Continuum

AbstractUnstable growth phenomena in spatially discrete wave equations are studied. We characterize sets of initial states leading to instability and collapse and obtain analytical predictions for the blow-up time. The theoretical predictions are con- trasted with the numerical solutions computed by a variety of schemes. The behavior of the systems in the continuum limit and the impact of discreteness and friction are discussed.

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