In this paper we consider a class of quasilinear, non-strictly hyper-bolic 2 2 systems in two space dimensions. Our main result is nite speed of propagation of the support of smooth solutions for these systems. As a consequence, we establish non-existence of global smooth solutions for a class of suuciently large, smooth initial data. The non-existence result applies to systems in conservation ...

and Applied Analysis 3 definition, it may happen that such a solution does not belong to any of the customary spaces of generalized functions. For example, given a function u : C \ {z0} −→ C 1.3 which is analytic everywhere except at the single point z0 ∈ C, and with an essential singularity at z0, Picard’s Theorem states that u attains every complex value, with possibly one exception, in every...

By using the theory of planar dynamical systems to a coupled non-linear wave equation, the existence of solitary wave solutions and uncountably infinite, many smooth and non-smooth, periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. 2003 Published by Elsevier Science Ltd.

In this paper, we employ the bifurcation theory of planar dynamical systems to investigate the exact travelling wave solutions of a generalized Degasperis-Procesi equation ut−uxxt+4uux+γ(u−uxx)x = 3uxuxx+uuxxx. The implicit expression of smooth soliton solutions is given. The explicit expressions of peaked soliton solutions and periodic cuspon solutions are also obtained. Further, we show the r...

We present evidence that the problem of breakdown/blowup of smooth solutions of the Euler and Navier-Stokes equations, is closely related to Hadamard’s concepts of wellposedness and illposedness. We present a combined criterion for blowup, based on detecting increasing L2-residuals and stability factors, which can be tested computationally on meshes of finite mesh size. 1 The Clay Navier-Stokes...

Abstract. This work is devoted to prove the exponential decay for the energy of solutions of the Korteweg-de Vries equation in a bounded interval with a localized damping term. Following the method in Menzala (2002) which combines energy estimates, multipliers and compactness arguments the problem is reduced to prove the unique continuation of weak solutions. In Menzala (2002) the case where so...

We find soliton solutions in five-dimensional gauged supergravity, where a circle degenerates smoothly in the core of the geometry. In the family of solutions we consider, we find no completely smooth supersymmetric solutions, but we find discrete families of non-supersymmetric solitons. We discuss the relation to previous studies of the asymptotically flat case. We also consider gauged supergr...

This is the third part of our project initiated in [LW1] on the study of the weakly convergent sequence of smooth (or certain classes of weak) solutions to the heat equation of harmonic maps or approximated harmonic maps (i.e. the negative gradient ow of the generalized Ginzburg-Landau functionals). The general situation for the heat ow of harmonic maps is as follows. Let un(x; t) : M R+ ! N be...