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Abstract We investigate the interaction of a pair of weakly nonlinear oscillators (eg. each near a Hopf bifurcation) when the coupling strength is comparable to the attraction of the limit cycles.… (More)

We consider a two-parameter family of maps of the plane to itself. Each map has a fixed point in the first quadrant and is a diffeomorphism in a neighborhood of this point. For certain parameter… (More)

(I) [ 4 = (u% + f(u) in (-L,L) X R+, u(tL,t)=O in R+, u(x, 0) = uo(x) in [-L,L], where m > 1 is a parameter, f is locally Lipschitz continuous, f(0) = 0, and u. is bounded. Problems of this form… (More)

Numerical simulation of periodic solutions in large arrays of Josephson junctions indicates the existence of periodic solutions where each junction oscillates with the same waveform, but with equal… (More)

AbstractWe study the regularity and the asymptotic behavior of the solutions of the initial value problem for the porous medium equation
$$\begin{gathered} {\text{ }}u_t = \left( {u^m } \right)_{xx}… (More)

- D. G. Aronson
- 1970

- D. G. Aronson, Gil, J. L. V´Zquez
- 1998

The paper is concerned with the behaviour of focusing solutions to nonlinear diffusion problems. These solutions describe the movement of a flow filling a hole and have consequences for the… (More)