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1994•SIAM Journal on Mathematical AnalysisRequires access

On a Globally Existing Solution to the Inviscid Burgers Equation with a Nonlocal Term

Kazuo Itô

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Abstract

It is shown that the inviscid Burgers equation with a nonlocal nonlinear term admits smooth global solutions for certain initial data which are smooth and nondecreasing. This result corresponds to a similar situation in the classical inviscid Burgers equation and is complementary to a result in a paper by R. Gardner [SIAM J. Math. Anal., 18 (1987), pp. 172–183].

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What this paper is about

It is shown that the inviscid Burgers equation with a nonlocal nonlinear term admits smooth global solutions for certain initial data which are smooth and nondecreasing. This result corresponds to a similar situation in the classical inviscid Burgers equation and is complementary to a result in a paper by R. Gardner [SIAM J. Math. Anal., 18 (1987), pp. 172–183].

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Available abstract

It is shown that the inviscid Burgers equation with a nonlocal nonlinear term admits smooth global solutions for certain initial data which are smooth and nondecreasing. This result corresponds to a similar situation in the classical inviscid Burgers equation and is complementary to a result in a paper by R. Gardner [SIAM J. Math. Anal., 18 (1987), pp. 172–183].

Key concepts: Inviscid flow, Burgers' equation, Mathematics, Term (time), Mathematical analysis, Nonlinear system, Partial differential equation, Classical mechanics

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