Viscosity solutions to a parabolic inhomogeneous equation associated with infinity Laplacian. (English) Zbl 1321.35104
Summary: We obtain the existence and uniqueness results of viscosity solutions to the initial and boundary value problem for a nonlinear degenerate and singular parabolic inhomogeneous equation of the form
\[
u_t - \Delta _\infty ^N u = f,
\]
where \(\Delta\infty^N\) denotes the so-called normalized infinity Laplacian given by \(\Delta _\infty ^N u = \frac{1} {| Du|^2}\langle D^2 uDu,Du\rangle \).
MSC:
| 35K65 | Degenerate parabolic equations |
| 35B51 | Comparison principles in context of PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 35K55 | Nonlinear parabolic equations |
| 35K57 | Reaction-diffusion equations |
| 35D40 | Viscosity solutions to PDEs |
Keywords:
parabolic equation; infinity Laplacian; viscosity solution; inhomogeneous equation; comparison principle; existenceReferences:
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