arXiv subjects

Carlos Banquet Brango

Publications and source records attributed to Carlos Banquet Brango.

3 recordsLinked to original sources

arXiv2018

Existence theory for the Boussinesq equation in Modulation spaces

In this paper we study the Cauchy problem for the generalized Boussinesq equation with initial data in modulation spaces $M^{s}_{p^\prime,q}(\mathbb{R}^n),$ $n\geq 1.$ After a decomposition of the Boussinesq equation in a $2\times 2$-nonlinear system, we obtain the existence of global and local solutions in several classes of functions with values in $ M^s_{p,q}\times D^{-1}JM^s_{p,q}$ spaces for suitable $p,q$ and $s,$ including the special case $p=2,q=1$ and $s=0.$ Finally, we prove some results of scattering and asymptotic stability in the framework of modulation spaces.

math.AP↗

arXiv2012

On the BBM-Burgers Equation: Well-posedness, Ill-posedness and Long Period Limit

In this work we study a dispersive equation with a dissipative term, the Benjamin-Bona-Mahony-Burgers equation. First we prove that the initial value problem for this equation is well-posed in $H^s(\mathbb{R}),$ for $s\geq 0$ and ill-posed if $s< 0.$ The ill-posedness is in the sense that the flow-map cannot be continuous at the origin from $H^s(\mathbb{R})$ to even $\mathcal{D}'(\mathbb{R}).$ Additionally, we establish an exact theory of convergence of the periodic solutions to the continuous one, in Sobolev spaces, as the period goes to infinity.

math.AP↗

arXiv2012

The Symmetric Regularized-Long-Wave Equation: Ill-posedness and Long Period Limit

In the present work we obtain two important results for the Symmetric Regulraized-Long-Wave equation. First we prove that the initial value problem for this equation is ill-posed for data in $H^s(\mathbb{R})\times H^{s-1}(\mathbb{R}),$ if $s< 0,$ in the sense that the flow-map cannot be continuous at the origin from $H^s(\mathbb{R})\times H^{s-1}(\mathbb{R})$ to even $(\mathcal{D}'(\mathbb{R}))^2.$ We also establish an exact theory of convergence of the periodic solutions to the continuous one, in Sobolev spaces, as the period goes to infinity.

math.AP↗