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Abstract
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We consider a class of degenerate parabolic systems in one space dimension; it
includes models for describing phenomena in consolidation, recovery and damage
prevention of building stones, involving diffusive processes arising only in some
regions. The question of existence of solutions is approached, by means of vanishing
viscosity, and entropy conditions holding for the solutions are presented.
Existence and uniqueness results for the approximating parabolic systems
are proved, taking into account the nonlinearity of the strongly coupled
equations.
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Keywords
degenerate parabolic systems, porous media, nonlinear
equations, vanishing viscosity, entropy solutions
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Mathematical Subject Classification
Primary: 35M11, 35M31
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Milestones
Received: 6 February 2025
Accepted: 23 March 2025
Published: 12 August 2025
Communicated by Roberto Natalini
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| © 2025 MSP (Mathematical Sciences
Publishers). |
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