5 edition of **Blowup for nonlinear hyperbolic equations** found in the catalog.

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- 0 Currently reading

Published
**1995**
by Birkhäuser in Boston
.

Written in English

- Differential equations, Hyperbolic -- Numerical solutions.,
- Cauchy problem.,
- Blowing up (Algebraic geometry)

**Edition Notes**

Includes bibliographical references (p. [107]-112) and index.

Statement | Serge Alinhac. |

Series | Progress in nonlinear differential equations and their applications ;, v. 17 |

Classifications | |
---|---|

LC Classifications | QA377 .A557 1995 |

The Physical Object | |

Pagination | xiv, 112 p. ; |

Number of Pages | 112 |

ID Numbers | |

Open Library | OL1271499M |

ISBN 10 | 0817638105, 3764338105 |

LC Control Number | 95002743 |

equations for an isentropic perfect ﬂuid. Due to the hyperbolic nature of these nonlinear equations, one expects singularity formation in the solutions. Indeed, one even expects black holes to form. However, singularity formation in relativistic ﬂow is not yet well-understood; the theory is most lacking in the multi-dimensional. The book can be divided into two parts. In the first part, the results on decay of solutions to nonlinear parabolic equations and hyperbolic parabolic coupled systems are obtained, and a chapter is devoted to the global existence of small smooth solutions to fully nonlinear parabolic equations and quasilinear hyperbolic parabolic coupled systems.

S. Alinhac, Blowup For Nonlinear Hyperbolic Equations, Progress in Nonlinear Differential Equations and their Applications 17 (Birkhäuser Boston, Boston, MA, ). Crossref, Google Scholar S. Alinhac, Journées "Équations aux Dérivées Partielles" (Universitié de Nantes, Nantes, ) p. Serge Alinhac is the author of Hyperbolic Partial Differential Equations ( avg rating, 0 ratings, 0 reviews, published ), Blowup for Nonlinear Hyp.

equation, the semilinear wave equation, the Korteweg-de Vries equation, and the wave maps equation. These four equations are of course only a very small sample of the nonlinear dispersive equations studied in the literature, but they are reasonably representative in that they showcase many of the techniques used for more general. By combining Song’s method and the concavity method, we studied some parabolic type equations and hyperbolic equations with damping terms. We also obtained the finite time blow-up result for certain solutions whose initial data have arbitrary high initial energy, see [20,21,22,23].

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The content of this book corresponds to a one-semester course taught at the Blowup for nonlinear hyperbolic equations book of Paris-Sud (Orsay) in the spring It is accessible to students or researchers with a basic elementary knowledge of Partial Dif ferential Equations, especially of hyperbolic PDE (Cauchy problem, wave operator, energy inequality, finite speed of propagation, symmetric systems, etc.).Cited by: Blowup for Nonlinear Hyperbolic Equations.

Authors (view affiliations) Serge Alinhac; Book. 74 Citations; k Downloads; Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 17) Log in to check access.

Buy eBook. USD Instant download; Readable on all devices. Blowup for Nonlinear Hyperbolic Equations. Authors: Alinhac, Serge Free Preview. Buy this book eB19 *immediately available upon purchase as print book shipments may be delayed due to the COVID crisis.

ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook : Birkhäuser Basel. A functional method for Burgers' equation.- b. Semilinear wave equation.- c. The Euler system.- 4. Blowup or not. Comparison and averaging methods.- Notes.- III.

Semilinear Wave Equations.- 1. Semilinear blowup criteria.- 2. Maximal influence domain.- 3. Maximal influence domains for weak solutions.- 4. Blowup rates at the boundary of the. COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

Based on an example of Jeffrey we next show how blowup for ordinary differential equations can be used to construct examples of blowup for systems of hyperbolic equations.

Finally we outline the construction of solutions to certain strictly hyperbolic 3 x 3-systems of conservation laws which blow up in either sup-norm or total variation norm in Author: Helge Kristian Jenssen, Carlo Sinestrari.

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The book first studies the particular self-similar. We prove nonexistence results for the Cauchy problem for the abstract hyperbolic equation in a Banach space X, u tt =f′(u), t>0; u(0)=u 0, u t (0)=u 1, where f: X→ R is a C l applications to the second- and higher-order hyperbolic equations with local and nonlocal nonlinearities are presented.

Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations.

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Google Scholar. Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type Kurokiba, Masaki and Ogawa, Takayoshi, Differential and Integral Equations, On a semi-linear system of nonlocal time and space reaction diffusion equations with exponential nonlinearities Ahmad, B., Alsaedi, A., Hnaien, D., and Kirane, M.

[1] S. Alinhac, Blowup for Nonlinear Hyperbolic ss in Nonlinear Differential Equations and their Applications, Birkhäuser Boston, Inc., Boston, MA. He is the author of Blowup for Nonlinear Hyperbolic Equations (Birkhäuser, ) and Pseudo-differential Operators and the Nash–Moser Theorem (with P.

Gérard, American Mathematical Society, ). His primary areas of research are linear and nonlinear partial differential equations. This paper deals with blow-up phenomena for an initial boundary value problem of a nonlocal quasilinear parabolic equation with time-dependent coefficients in a bounded star-shaped region under nonlinear boundary flux.

Using the auxiliary function method and modified differential inequality technique, we establish some conditions on time-dependent coefficients and nonlinearities to guarantee. The equations of general relativ-ity, the Einstein equations, are essentially hyperbolic in nature and the study of spacetime singularities is naturally related to blow-up phenom-ena for nonlinear hyperbolic systems.

These connections are explained and recent progress in applying the theory of hyperbolic equations in this ﬁeld is presented. We consider the initial value problem with boundary control for a scalar nonlinear conservation law \begin{equation*} u_t+[f(u)]_x=0,\qquad\qquad u(0,x)=0,\qquad u.

Part 5 Nonlinear geometrical optics and applications: quasilinear systems in one space dimension - formal analysis, slow time and reduced equations, existence, approximation and blowup quasilinear. Dinlemez proved the global existence and uniqueness of weak solutions for the initial-boundary value problem for a nonlinear wave equation with strong structural damping and nonlinear source terms in.

A lot of papers in connection with blow-up, global solutions and existence of weak solutions were studied in. Blowup for nonlinear hyperbolic equations, volume 17 of Progress in Nonlinear Differential Equations and their Applications. Birkhäuser Boston Inc., Boston, MA, B. Dodson, A.

Lawrie. Scattering for radial, semi-linear, super-critical wave equations with bounded critical norm. preprint arXiv.

Zhou, “A blow-up result for a nonlinear wave equation with damping and vanishing initial energy in R n,” Applied Mathematics Letters, vol. 18, no. 3, pp. –, In this paper we study the asymptotic behavior of solutions for a free boundary problem modeling the growth of tumors containing two species of cells: proliferating cells and quiescent cells.

This.survey by c ([2]) for more details on blow-up results for nonlinear hyperbolic contrast to parabolic equations, it seems that there is a little work devoted to asymptotic proﬁles and blow-up rates of blow-up solutions for hyperbolic ore, numerical methods would be.