Shock formation for the forced burgers equation and an application

Misha L. Bialy

doi:10.1007/PL00001636

Shock formation for the forced burgers equation and an application

Misha L. Bialy^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We study the inviscid Burgers equation in the presence of spatially periodic non-zero potential force. We prove that for the foliated initial value problem there are always solutions developing shocks in a finite time. We give an application of this result to a quasi-linear system of conservation laws which appeared in the study of integrable Hamiltonian systems with 1.5 degrees of freedom.

Original language	English
Pages (from-to)	732-740
Number of pages	9
Journal	Geometric and Functional Analysis
Volume	10
Issue number	4
DOIs	https://doi.org/10.1007/PL00001636
State	Published - 2000

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title = "Shock formation for the forced burgers equation and an application",

abstract = "We study the inviscid Burgers equation in the presence of spatially periodic non-zero potential force. We prove that for the foliated initial value problem there are always solutions developing shocks in a finite time. We give an application of this result to a quasi-linear system of conservation laws which appeared in the study of integrable Hamiltonian systems with 1.5 degrees of freedom.",

author = "Bialy, {Misha L.}",

note = "Funding Information: The author was partially supported by EPSRC.",

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doi = "10.1007/PL00001636",

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AU - Bialy, Misha L.

N1 - Funding Information: The author was partially supported by EPSRC.

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N2 - We study the inviscid Burgers equation in the presence of spatially periodic non-zero potential force. We prove that for the foliated initial value problem there are always solutions developing shocks in a finite time. We give an application of this result to a quasi-linear system of conservation laws which appeared in the study of integrable Hamiltonian systems with 1.5 degrees of freedom.

AB - We study the inviscid Burgers equation in the presence of spatially periodic non-zero potential force. We prove that for the foliated initial value problem there are always solutions developing shocks in a finite time. We give an application of this result to a quasi-linear system of conservation laws which appeared in the study of integrable Hamiltonian systems with 1.5 degrees of freedom.

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U2 - 10.1007/PL00001636

DO - 10.1007/PL00001636

M3 - מאמר

AN - SCOPUS:0034359128

VL - 10

SP - 732

EP - 740

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

SN - 1016-443X

IS - 4

ER -

Shock formation for the forced burgers equation and an application

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