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  1. Zeitschrift für angewandte Mathematik und Physik
  2. Zeitschrift für angewandte Mathematik und Physik : Volume 58
  3. Zeitschrift für angewandte Mathematik und Physik : Volume 58, Issue 4, July 2007
  4. The self-similar solutions of the Tricomi-type equations
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Zeitschrift für angewandte Mathematik und Physik : Volume 67
Zeitschrift für angewandte Mathematik und Physik : Volume 66
Zeitschrift für angewandte Mathematik und Physik : Volume 65
Zeitschrift für angewandte Mathematik und Physik : Volume 64
Zeitschrift für angewandte Mathematik und Physik : Volume 63
Zeitschrift für angewandte Mathematik und Physik : Volume 62
Zeitschrift für angewandte Mathematik und Physik : Volume 61
Zeitschrift für angewandte Mathematik und Physik : Volume 60
Zeitschrift für angewandte Mathematik und Physik : Volume 59
Zeitschrift für angewandte Mathematik und Physik : Volume 58
Zeitschrift für angewandte Mathematik und Physik : Volume 58, Issue 6, November 2007
Zeitschrift für angewandte Mathematik und Physik : Volume 58, Issue 5, September 2007
Zeitschrift für angewandte Mathematik und Physik : Volume 58, Issue 4, July 2007
Solitary waves and their linear stability in weakly coupled KdV equations
Traveling fronts in diffusive and cooperative Lotka–Volterra system with nonlocal delays
Homogenization of a convection–diffusion equation in perforated domains with a weak adsorption
The self-similar solutions of the Tricomi-type equations
Flow past a porous approximate spherical shell
Finite homogeneous deformations of symmetrically loaded compressible membranes
Agmon’s condition for incompressible elasticity: A formulation of Mielke–Sprenger type
Hyperbolic system of balance laws modeling dissipative ionic crystals
Buchbesprechungen – Book reviews – Notices bibliographiques
Zeitschrift für angewandte Mathematik und Physik : Volume 58, Issue 3, May 2007
Zeitschrift für angewandte Mathematik und Physik : Volume 58, Issue 2, March 2007
Zeitschrift für angewandte Mathematik und Physik : Volume 58, Issue 1, January 2007
Zeitschrift für angewandte Mathematik und Physik : Volume 57
Zeitschrift für angewandte Mathematik und Physik : Volume 56
Zeitschrift für angewandte Mathematik und Physik : Volume 55
Zeitschrift für angewandte Mathematik und Physik : Volume 54
Zeitschrift für angewandte Mathematik und Physik : Volume 53
Zeitschrift für angewandte Mathematik und Physik : Volume 52
Zeitschrift für angewandte Mathematik und Physik : Volume 51
Zeitschrift für angewandte Mathematik und Physik : Volume 50
Zeitschrift für angewandte Mathematik und Physik : Volume 49
Zeitschrift für angewandte Mathematik und Physik : Volume 48

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The self-similar solutions of the Tricomi-type equations

Content Provider SpringerLink
Author Yagdjian, Karen
Copyright Year 2006
Abstract This paper analyses the properties of the family of self-similar solutions of the generalized Tricomi equation $$u_{{tt}} - t^{{2k}} \Delta u = 0\,(2k \in {{\mathbb{N}}})$$ in the domain $${{\mathbb{R}}}_{ + }^{{1 + n}}$$ by considering initial conditions on the functions and their derivatives, posed as the Cauchy problem with homogeneous initial data. For specific values of the power k ( = 1/2 or = 3/2) and n = 1 this problem has applications in the aerodynamics of airfoils operating in transonic flows of perfect or dense gases, respectively. An integral transformation is suggested and used to represent the solutions of the Cauchy problem with homogeneous initial functions in terms of fundamental solutions of the classical wave equation (the case k = 0). Then the Cauchy problem with homogeneous initial functions for the wave equation in $${{\mathbb{R}}}^{{1 + n}}$$ is solved. These results are used to derive estimates of the upper bound for solutions’ size and to obtain the asymptotics for self-similar solutions of the wave equation and of the Tricomi-type equation in the neighbourhood of their light cones.
Ending Page 645
Page Count 34
Starting Page 612
File Format PDF
ISSN 00442275
e-ISSN 14209039
Journal Zeitschrift für angewandte Mathematik und Physik
Issue Number 4
Volume Number 58
Language English
Publisher Birkhäuser-Verlag
Publisher Date 2006-11-29
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Mathematical Methods in Physics Nonlinear second-order hyperbolic equations Tricomi-type equations Theoretical and Applied Mechanics Tricomi equation self-similar solutions Degenerate hyperbolic equations Initial value problems for second-order hyperbolic equations
Content Type Text
Resource Type Article
Subject Applied Mathematics Physics and Astronomy
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