On the structure of weak solutions to the Riemann problem for degenerate nonlinear diffusion equation

2022/10/29 by Evgeny Yu. Panov, Panov, Evgeny Yu.
Computer Science · Mathematics · #35C06 #35D30 #35K58 #35K65 #35R35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2210.16546

openalex publication_date 2022/10/29 · openalex created_date 2022/11/06 · openalex updated_date 2026/07/28

Abstract

We find an explicit form of weak solutions to a Riemann problem for a degenerate semilinear parabolic equation with piecewise constant diffusion coefficient. It is demonstrated that the phase transition lines (free boundaries) correspond to the minimum point of some strictly convex function of a finite number of variables. In the limit as number of phases tend to infinity we obtain a variational formulation of self-similar solution with an arbitrary nonnegative diffusion function.

Related

• On the structure of entropy solutions to the Riemann problem for a degenerate nonlinear parabolic equation
• Degenerate nonlinear parabolic equations with discontinuous diffusion\n coefficients
• On the Theory of Discontinuous Solutions to Some Strongly Degenerate Parabolic Equations
• Asymptotics of Fundamental Solution of Cauchy Problem for Parabolic Equation with Small Parameter and Degeneration
• On the Dynamics of a Degenerate Parabolic Equation: Global Bifurcation of Stationary States and Convergence