open access

https://doi.org/10.14943/83477

https://hdl.handle.net/2115/69081

Evolving graphs by singular weighted curvature

英語

1996-03-01

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

331

1-94

A new notion of solutions is introduced to study degenerate non­linear parabolic equations in one space dimension whose diffusion effect is so strong at particular slopes of unknowns that the equation is no longer a partial differential equation. Extending the theory of viscosity solutions comparison principle is established. For a periodic continuous initial data a unique global continuous solution (periodic in space) is constructed. The theory applies to motion of interfacial curves by crystalline energy or more generally by anisotropic interlacial energy with corners when the curves are the graphs of functions. Even if the driving force term exists, the initial value problem is solvable for general nonadmissible continuous (periodic) initial data.

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