6533b82cfe1ef96bd128ea18

RESEARCH PRODUCT

Strong solutions to a parabolic equation with linear growth with respect to the gradient variable

Flavia SmarrazzoSalvador Moll

subject

Minimal surfaceGeneralizationApplied Mathematics010102 general mathematicsMathematical analysis01 natural sciences010101 applied mathematicsStrong solutionsNeumann boundary conditionLimit (mathematics)Uniqueness0101 mathematicsLinear growthAnalysisVariable (mathematics)Mathematics

description

Abstract In this paper we prove existence and uniqueness of strong solutions to the homogeneous Neumann problem associated to a parabolic equation with linear growth with respect to the gradient variable. This equation is a generalization of the time-dependent minimal surface equation. Existence and regularity in time of the solution is proved by means of a suitable pseudoparabolic relaxed approximation of the equation and a passage to the limit.

yearjournalcountryeditionlanguage
2018-06-01Journal of Differential Equations
https://doi.org/10.1016/j.jde.2018.01.050