Displaying similar documents to “Breakdown in finite time of solutions to a one-dimensional wave equation.”

Global existence and decay of solutions of a coupled system of BBM-Burgers equations.

Jardel Morais Pereira (2000)

Revista Matemática Complutense

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The global well-posedness of the initial-value problem associated to the coupled system of BBM-Burgers equations (*) in the classical Sobolev spaces H(R) x H(R) for s ≥ 2 is studied. Furthermore we find decay estimates of the solutions of (*) in the norm L(R) x L(R), 2 ≤ q ≤ ∞ for general initial data. Model (*) is motivated by a work due to Gear and Grimshaw [10] who considered strong interaction of weakly nonlinear long waves governed by a coupled system of KdV equations.

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.