Vortrag von Mag. Rainer Brunnhuber am 28.01.2014

Einladung zum Vortrag von

Mag. Rainer Brunnhuber

(AAU, Institut Mathematik)

zu dem Thema

On some methods in nonlinear partial differential equations and their applications to the Blackstock-Crighton-Westervelt rotational model equation


Ort: V.1.04

Zeit: Dienstag, 28.01.2014, 16:00 Uhr s. t.

Abstract:

We consider the Blackstock-Crighton rotational model equation which is a fourth-order in space and third-order in time nonlinear partial differential equation and arises in the context of the modeling of nonlinear acoustic wave propagation in thermally relaxing viscous fluids.

We use the theory of operator semigroups to investigate the linearization of the equation and show that the underlying semigroup is analytic which, together with a negative spectral bound of its generator, leads to exponential decay results for the linear homogeneous equation.

Moreover, invoking the Banach fixed-point theorem, we prove local well-posedness of the Blackstock-Crighton model for sufficiently small initial data.

Finally, we show how barrier’s method is used to obtain global in time well-posedness and provide exponential decay results also for the nonlinear equation.

Share
Tags »

Autor:
Datum: Dienstag, 21. Januar 2014 11:15
Trackback: Trackback-URL Themengebiet: Institut, MATH, Veranstaltung

Feed zum Beitrag: RSS 2.0 Diesen Artikel kommentieren

Kommentar abgeben