Behavior of critical solutions of a nonlocal hyperbolic problem in Ohmic heating of foods.
Best approximation and the numerical solution of partial differential equations with the tau method
Bifurcation of free vibrations for completely resonant wave equations
We prove existence of small amplitude, 2p/v-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem.
Bifurcations near a double eigenvalue of the rectangular plate problem with a domain parametr
Bilinear space-time estimates for homogeneous wave equations
Blow up of solutions for Klein-Gordon equations in the Reissner-Nordstrom metric.
Blow up of solutions to semilinear wave equations.
Blow up of solutions with positive energy in nonlinear thermoelasticity with second sound.
Blow up of the solutions of nonlinear wave equation.
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 for nonlinear wave equations with slowly decaying data.
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...
Blowup of small data solutions for a quasilinear wave equation in two space dimensions.
Blow-up of solutions for a system of nonlinear wave equations with nonlinear damping.
Blow-up of solutions for a viscoelastic equation with nonlinear damping
The initial boundary value problem for a viscoelastic equation with nonlinear damping in a bounded domain is considered. By modifying the method, which is put forward by Li, Tasi and Vitillaro, we sententiously proved that, under certain conditions, any solution blows up in finite time. The estimates of the life-span of solutions are also given. We generalize some earlier results concerning this equation.
Blow-up of solutions for an integro-differential equation with a nonlinear source.
Blowup of solutions for evolution equations with nonlinear damping.
Blow-up of solutions for the Kirchhoff equation of q-Laplacian type with nonlinear dissipation
We establish the blow-up of solutions to the Kirchhoff equation of q-Laplacian type with a nonlinear dissipative term , x ∈ Ω, t > 0.
Blowup of solutions of a nonlinear wave equation.