Blowup analysis for a semilinear parabolic system with nonlocal boundary condition.
Blowup and asymptotic stability of weak solutions to wave equations with nonlinear degenerate damping and source terms.
Blow-up and global existence of a weak solution for a sine-Gordon type quasilinear wave equation
Si considera il problema di Cauchy per l'equazione (cf. [1]): Nella prima parte di questo articolo si dimostra, per dati iniziali particolari, un risultato di «blow-up» della soluzione classica locale (in tempo), seguendo le idee introdotte in [8], [2] ed [4]. Nella seconda parte, viene utilizzato il metodo di compattezza per compensazione (cf. [13], [10] ed [5]) ed una estensione del principio delle regioni invarianti (cf. [12]) per dimostrare l'esistenza di una soluzione debole globale entropica....
Blow-up and global existence profile of a class of fully nonlinear degenerate parabolic equations
This paper is mainly concerned with the blow-up and global existence profile for the Cauchy problem of a class of fully nonlinear degenerate parabolic equations with reaction sources.
Blowup and life span bounds for a reaction-diffusion equation with a time-dependent generator.
Blow-up and nonexistence of sign changing solutions to the Brezis–Nirenberg problem in dimension three
Blow-up behavior in nonlocal vs local heat equations
We present some recent results on the blow-up behavior of solutions of heat equations with nonlocal nonlinearities. These results concern blow-up sets, rates and profiles. We then compare them with the corresponding results in the local case, and we show that the two types of problems exhibit "dual" blow-up behaviors.
Blow-up behaviour of one-dimensional semilinear parabolic equations
Blow-up boundary solutions for quasilinear anisotropic equations.
Blowup estimates for a mutualistic model in ecology.
Blow-up for 3-D compressible isentropic Navier-Stokes-Poisson equations
We study compressible isentropic Navier-Stokes-Poisson equations in . With some appropriate assumptions on the density, velocity and potential, we show that the classical solution of the Cauchy problem for compressible unipolar isentropic Navier-Stokes-Poisson equations with attractive forcing will blow up in finite time. The proof is based on a contradiction argument, which relies on proving the conservation of total mass and total momentum.
Blow-up for a localized singular parabolic equation with weighted nonlocal nonlinear boundary conditions
This paper deals with the blow-up properties of positive solutions to a localized singular parabolic equation with weighted nonlocal nonlinear boundary conditions. Under certain conditions, criteria of global existence and finite time blow-up are established. Furthermore, when q=1, the global blow-up behavior and the uniform blow-up profile of the blow-up solution are described; we find that the blow-up set is the whole domain [0,a], including the boundary, in contrast to the case of parabolic equations...
Blowup for a non-Newtonian polytropic filtration system coupled via nonlinear boundary flux.
Blowup for degenerate and singular parabolic equation with nonlocal source.
Blowup for degenerate and singular parabolic system with nonlocal source.
Blow-up for nonlinear wave equations with slowly decaying data.
Blow-up for p-Laplacian parabolic equations.
Blow-up for solutions of hyperbolic PDE and spacetime singularities
An important question in mathematical relativity theory is that of the nature of spacetime singularities. The equations of general relativity, the Einstein equations, are essentially hyperbolic in nature and the study of spacetime singularities is naturally related to blow-up phenomena for nonlinear hyperbolic systems. These connections are explained and recent progress in applying the theory of hyperbolic equations in this field is presented. A direction which has turned out to be fruitful is that...
Blow-up for the compressible isentropic Navier-Stokes-Poisson equations
We will show the blow-up of smooth solutions to the Cauchy problems for compressible unipolar isentropic Navier-Stokes-Poisson equations with attractive forcing and compressible bipolar isentropic Navier-Stokes-Poisson equations in arbitrary dimensions under some restrictions on the initial data. The key of the proof is finding the relations between the physical quantities and establishing some differential inequalities.
Blow-up for the energy-critical nonlinear wave equation and Schrödinger equation with inverse-square potential
We give a sufficient condition under which the solutions of the energy-critical nonlinear wave equation and Schrödinger equation with inverse-square potential blow up. The method is a modified variational approach, in the spirit of the work by Ibrahim et al. [Anal. PDE 4 (2011), 405-460].