The Cauchy problem for ut= Δu+|∇ u| q

With q a positive real number, the nonlinear partial differential equation in the title of the paper arises in the study of the growth of surfaces. In that context it is known as the generalized deterministic KPZ equation. The paper is concerned with the initial-value problem for the equation under...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2003-08, Vol.284 (2), p.733-755
Main Authors: Gilding, Brian H., Guedda, Mohammed, Kersner, Robert
Format: Article
Language:English
Subjects:
Existence
KPZ equation
Nonlinear
Parabolic
Regularity
Surface growth
Uniqueness
Viscous Hamilton–Jacobi equation
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Summary:With q a positive real number, the nonlinear partial differential equation in the title of the paper arises in the study of the growth of surfaces. In that context it is known as the generalized deterministic KPZ equation. The paper is concerned with the initial-value problem for the equation under the assumption that the initial-data function is bounded and continuous. Results on the existence, uniqueness, and regularity of solutions are obtained.
ISSN:0022-247X
1096-0813
DOI:10.1016/S0022-247X(03)00395-0