An oscillation free local discontinuous Galerkin method for nonlinear degenerate parabolic equations [PDF]
Numerical Methods for Partial Differential Equations, 2021 An oscillation free local discontinuous Galerkin (OFLDG) method is proposed for solving nonlinear degenerate parabolic equations. The damping terms are added to the original LDG scheme to control the spurious oscillations when solutions have a large ...
Q. Tao +3 more
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On Two Coupled Degenerate Parabolic Equations Motivated by Thermodynamics [PDF]
Journal of nonlinear science, 2021 We discuss a system of two coupled parabolic equations that have degenerate diffusion constants depending on the energy-like variable. The dissipation of the velocity-like variable is fed as a source term into the energy equation leading to conservation ...
A. Mielke
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Existence results for some nonlinear parabolic equations with degenerate coercivity and singular lower-order terms [PDF]
Mathematica Bohemica, 2023 In this paper, we study the existence results for some parabolic equations with degenerate coercivity, singular lower order term depending on the gradient, and positive initial data in $L^1$.
Rabah Mecheter, Fares Mokhtari
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Null controllability of strongly degenerate parabolic equations
E S A I M: Control, Optimisation and Calculus of Variations, 2023 We consider linear one-dimensional strongly degenerate parabolic equations with measurable coefficients that may be degenerate or singular. Taking 0 as the point where the strong degeneracy occurs, we assume that the coefficient a = a(x) in the principal
L. Rosier, Antoine Benoit, R. Loyer
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Classification of nonnegative traveling wave solutions for the 1D degenerate parabolic equations
Discrete and Continuous Dynamical Systems - B, 2022 Traveling wave solutions for the one-dimensional degenerate parabolic equations are considered. The purpose of this paper is to classify the nonnegative traveling wave solutions including sense of weak solutions of these equations and to present their ...
Yutaka Ichida
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WENO schemes for multidimensional nonlinear degenerate parabolic PDEs [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2018 In this paper, a scheme is presented for approximating solutions of non linear degenerate parabolic equations which may contain discontinuous solutions.
R. Abedian
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Trace formulae of potentials for degenerate parabolic equations [PDF]
Differential and Integral Equations, 2020 In this paper, we analyze main properties of the volume and layer potentials as well as the Poisson integral for a multi-dimensional degenerate parabolic equation.
Mukhtar Karazym, D. Suragan
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Uniqueness for degenerate parabolic equations in weighted $$L^1$$ spaces [PDF]
Journal of evolution equations (Printed ed.), 2020 We study uniqueness of solutions to degenerate parabolic problems, posed in bounded domains, where no boundary conditions are imposed. Under suitable assumptions on the operator, uniqueness is obtained for solutions that satisfy an appropriate integral ...
Camilla Nobili, F. Punzo
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A priori estimate of the solution of the Cauchy problem in the Sobolev classes for discontinuous coefficients of degenerate heat equations [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2022 Partial differential equations of the parabolic type with discontinuous coefficients and the heat equation degenerating in time, each separately, have been well studied by many authors.
U.K. Koilyshov +2 more
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Nonnegative controllability for a class of nonlinear degenerate parabolic equations with application to climate science [PDF]
Electronic Journal of Differential Equations, 2020 We consider a nonlinear degenerate reaction-diffusion equation. First we prove that if the initial state is nonnegative, then the solution remains nonnegative for all time.
Giuseppe Floridia
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