Advances in Differential Equations

The mixed Cauchy-Dirichlet problem for a viscous Hamilton-Jacobi equation

Said Benachour and Simona Dabuleanu

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We study the existence, uniqueness, and regularity of weak solutions for a viscous Hamilton-Jacobi equation of the form: $u_t-\Delta u=a|\nabla u|^p, $ $p\in(0,\infty)$ and $a\in{{\bf R}}$, $a\neq 0$, with Dirichlet boundary condition and irregular initial data $\mu_0$. The cases of initial data $\mu_0$ a bounded Radon measure, or a function in the Lebesgue space $L^q, 1\leq q < \infty$ are investigated.

Article information

Adv. Differential Equations, Volume 8, Number 12 (2003), 1409-1452.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B33: Critical exponents 35B65: Smoothness and regularity of solutions 35D05 35K20: Initial-boundary value problems for second-order parabolic equations


Benachour, Said; Dabuleanu, Simona. The mixed Cauchy-Dirichlet problem for a viscous Hamilton-Jacobi equation. Adv. Differential Equations 8 (2003), no. 12, 1409--1452.

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