Differential and Integral Equations

The Hopf-Lax formula gives the unique viscosity solution

Thomas Strömberg

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Abstract

It is proved that the Hopf--Lax formula provides the unique viscosity solution of the Cauchy problem \begin{align*} u'_t(t,x)+H(u'_x(t,x)) & =0, \qquad(t,x)\in(0,T]\times {\bf R}^n,\\ \lim_{t\downarrow0} u(t,x) & =\varphi(x)\qquad\text{for all $x\in {\bf R}^n$.} \end{align*}

Article information

Source
Differential Integral Equations, Volume 15, Number 1 (2002), 47-52.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060882

Mathematical Reviews number (MathSciNet)
MR1869821

Zentralblatt MATH identifier
1026.49023

Subjects
Primary: 49L25: Viscosity solutions
Secondary: 35F20: Nonlinear first-order equations

Citation

Strömberg, Thomas. The Hopf-Lax formula gives the unique viscosity solution. Differential Integral Equations 15 (2002), no. 1, 47--52. https://projecteuclid.org/euclid.die/1356060882


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