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Instability of oscillations in cable-stayed bridges

Josef Malík (2005)

Applications of Mathematics

In this paper the stability of two basic types of cable stayed bridges, suspended by one or two rows of cables, is studied. Two linearized models of the center span describing the vertical and torsional oscillations are investigated. After the analysis of these models, a stability criterion is formulated. The criterion expresses a relation between the eigenvalues of the vertical and torsional oscillations of the center span. The continuous dependence of the eigenvalues on some data is studied and...

Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension

Frank Merle, Hatem Zaag (2009/2010)

Séminaire Équations aux dérivées partielles

We consider the semilinear wave equation with power nonlinearity in one space dimension. We first show the existence of a blow-up solution with a characteristic point. Then, we consider an arbitrary blow-up solution u ( x , t ) , the graph x ↦ T ( x ) of its blow-up points and 𝒮 ⊂ ℝ the set of all characteristic points and show that 𝒮 is locally finite. Finally, given x 0 ∈ 𝒮 , we show that in selfsimilar variables, the solution decomposes into a decoupled sum of (at least two) solitons, with alternate signs and that T ( x ) forms a...

Klein-Gordon type decay rates for wave equations with time-dependent coefficients

Michael Reissig, Karen Yagdjian (2000)

Banach Center Publications

This work is concerned with the proof of L p - L q decay estimates for solutions of the Cauchy problem for the Klein-Gordon type equation u t t - λ 2 ( t ) b 2 ( t ) ( Δ u - m 2 u ) = 0 . The coefficient consists of an increasing smooth function λ and an oscillating smooth and bounded function b which are uniformly separated from zero. Moreover, m 2 is a positive constant. We study under which assumptions for λ and b one can expect as an essential part of the decay rate the classical Klein-Gordon decay rate n/2(1/p-1/q).

Liouville type theorem for solutions of linear partial differential equations with constant coefficients

Akira Kaneko (2000)

Annales Polonici Mathematici

We discuss existence of global solutions of moderate growth to a linear partial differential equation with constant coefficients whose total symbol P(ξ) has the origin as its only real zero. It is well known that for such equations, global solutions tempered in the sense of Schwartz reduce to polynomials. This is a generalization of the classical Liouville theorem in the theory of functions. In our former work we showed that for infra-exponential growth the corresponding assertion is true if and...

Liouville type theorems for φ-subharmonic functions.

Marco Rigoli, Alberto G. Setti (2001)

Revista Matemática Iberoamericana

In this paper we present some Liouville type theorems for solutions of differential inequalities involving the φ-Laplacian. Our results, in particular, improve and generalize known results for the Laplacian and the p-Laplacian, and are new even in these cases. Phragmen-Lindeloff type results, and a weak form of the Omori-Yau maximum principle are also discussed.

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