Displaying similar documents to “On the nonhamiltonian character of shocks in 2-D pressureless gas”

On the existence of shock propagation in a flow through deformable porous media

E. Comparini, M. Ughi (2002)

Bollettino dell'Unione Matematica Italiana

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We consider a one-dimensional incompressible flow through a porous medium undergoing deformations such that the porosity and the hydraulic conductivity can be considered to be functions of the flux intensity. The medium is initially dry and we neglect capillarity, so that a sharp wetting front proceeds into the medium. We consider the open problem of the continuation of the solution in the case of onset of singularities, which can be interpreted as a local collapse of the medium, in...

Breakdown in finite time of solutions to a one-dimensional wave equation.

Mokhtar Kirane, Salim A. Messaoudi (2000)

Revista Matemática Complutense

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We consider a special type of a one-dimensional quasilinear wave equation w - phi (w / w) w = 0 in a bounded domain with Dirichlet boundary conditions and show that classical solutions blow up in finite time even for small initial data in some norm.

Blow-up and global existence of a weak solution for a sine-Gordon type quasilinear wave equation

João-Paulo Dias, Mário Figueira (2000)

Bollettino dell'Unione Matematica Italiana

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Si considera il problema di Cauchy per l'equazione (cf. [1]): ϕ t ⁢ t - ϕ x ⁢ x - ϕ x 2 ⁢ ϕ x ⁢ x + sin ⁡ ϕ = 0 ⁢ x , t ∈ R × R + . 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...

Formation of Singularities for Weakly Non-Linear N×N Hyperbolic Systems

Boiti, Chiara, Manfrin, Renato (2001)

Serdica Mathematical Journal

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We present some results on the formation of singularities for C^1 - solutions of the quasi-linear N × N strictly hyperbolic system Ut + A(U )Ux = 0 in [0, +∞) × Rx . Under certain weak non-linearity conditions (weaker than genuine non-linearity), we prove that the first order derivative of the solution blows-up in finite time.