What question did this study set out to answer?

To investigate the conditions under which solutions exist or do not exist for a class of nonlinear parabolic equations with singular boundary conditions.

February 9, 2026Open Access

Singular Dirichlet boundary problems for a class of fully nonlinear parabolic equations in one dimension

Key Points

To investigate the conditions under which solutions exist or do not exist for a class of nonlinear parabolic equations with singular boundary conditions.
Analysis of fully nonlinear parabolic equations with specific boundary conditions.
Focus on the p-Laplace type heat equation and curvature flow.
Examination of the dependence on the initial function's boundedness.
Found that solutions' existence heavily depends on the properties of the interior equation.
Identified scenarios where non-existence of solutions occurs based on boundary conditions.
Demonstrated how the initial function's boundedness influences solution outcomes.

Abstract

Abstract In this paper, we deal with the initial value problem for a class of fully nonlinear parabolic equations with a singular Dirichlet boundary condition in one space dimension. The interior equation includes, for example, a fully nonlinear p -Laplace type heat equation and a β -power type curvature flow. The singular Dirichlet boundary condition depicts, for example, the asymptoticness of the ends of complete curves to parallel two lines in geometric flow of graphs. We study the dependence of the existence and non-existence of solutions to the problem on the interior equation and the boundedness of the initial function.

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Cite This Study

Takashi Kagaya (Thu,) studied this question.

synapsesocial.com/papers/69897a86f0ec2af6756e8a3a https://doi.org/https://doi.org/10.1007/s00208-026-03334-7

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