Strong traces to degenerate parabolic equations
Marko Erceg, Darko Mitrovi\'c
TL;DR
This paper establishes the existence of strong traces at initial time for quasi-solutions to multidimensional degenerate parabolic equations without non-degeneracy assumptions, using a novel combination of blow-up and precompactness techniques.
Contribution
It introduces a new method combining blow-up and induction to prove strong trace existence for degenerate parabolic equations without non-degeneracy conditions.
Findings
Proves existence of strong traces at t=0 for quasi-solutions.
Develops a combined blow-up and induction approach.
Extends trace results to multidimensional degenerate equations.
Abstract
We prove existence of strong traces at for quasi-solutions to (multidimensional) degenerate parabolic equations with no non-degeneracy conditions. In order to solve the problem, we combine the blow up method and a strong precompactness result for quasi-solutions to degenerate parabolic equations with the induction argument with respect to the space dimension.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Stability and Controllability of Differential Equations