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$L^{1}$ existence and uniqueness results for quasi-linear elliptic equations with nonlinear boundary conditions

F. Andreu; N. Igbida; J. M. Mazón; J. Toledo — 2007

Annales de l'I.H.P. Analyse non linéaire

Erratum: A Parabolic Quasilinear Problem for Linear Growth Functionals.

F. Andreu; V. Caselles; J. M. Mazón — 2008

Revista Matemática Iberoamericana

The Cauchy problem for a strongly degenerate quasilinear equation

F. Andreu; Vicent Caselles; J. M. Mazón — 2005

Journal of the European Mathematical Society

We prove existence and uniqueness of entropy solutions for the Cauchy problem for the quasilinear parabolic equation $u_{t} = div 𝐚 (u, D u)$ , where $𝐚 (z, ξ) = \nabla_{ξ} f (z, ξ)$ , and $f$ is a convex function of $ξ$ with linear growth as $∥ ξ ∥ \to \infty$ , satisfying other additional assumptions. In particular, this class includes a relativistic heat equation and a flux limited diffusion equation used in the theory of radiation hydrodynamics.

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$L^{1}$ existence and uniqueness results for quasi-linear elliptic equations with nonlinear boundary conditions

Erratum: A Parabolic Quasilinear Problem for Linear Growth Functionals.

The Cauchy problem for a strongly degenerate quasilinear equation

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Currently displaying 1 – 3 of 3

L 1 existence and uniqueness results for quasi-linear elliptic equations with nonlinear boundary conditions

Erratum: A Parabolic Quasilinear Problem for Linear Growth Functionals.

The Cauchy problem for a strongly degenerate quasilinear equation

$L^{1}$ existence and uniqueness results for quasi-linear elliptic equations with nonlinear boundary conditions