Characterizations and properties of solutions to parabolic problems of linear growth

2025/05/22 by Theo Elenius, Elenius, Theo
Mathematics · Computer Science · #Nonlinear Differential Equations Analysis #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2505.16747

Abstract

We consider notions of weak solutions to a general class of parabolic problems of linear growth, formulated independently of time regularity. Equivalence with variational solutions is established using a stability result for weak solutions. A key tool in our arguments is approximation of parabolic BV functions using time mollification and Sobolev approximations. We also prove a comparison principle and a local boundedness result for solutions. When the time derivative of the solution is in L² our definitions are equivalent with the definition based on the Anzellotti pairing.

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