Convergence for Degenerate Parabolic Equations
Journal of Differential Equations, 1999 AbstractWe prove that any bounded global solution to a degenerate parabolic problem in one spatial dimension converges to a unique stationary state.
Frédérique Simondon, Eduard Feireisl
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Degenerate parabolic equations appearing in atmospheric dispersion of pollutants
Electronic Journal of Qualitative Theory of Differential Equations, 2016 Linear and nonlinear degenerate abstract parabolic equations with variable coefficients are studied. Here the equation and boundary conditions are degenerated on all boundary and contain some parameters.
Veli Shakhmurov, Aida Sahmurova
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Determination of the right-hand side term in the degenerate parabolic equation with two variables
Journal of Physics: Conference Series, 2019 We find two type conditions sufficient for unique solvability of inverse problem of source determination in degenerate parabolic equation with two independent variables.
V. Kamynin, A. Kostin
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A new kind of the solution of degenerate parabolic equation with unbounded convection term
Open Mathematics, 2015 A new kind of entropy solution of Cauchy problem of the strong degenerate parabolic ...
Huashui Zhan
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Pullback Attractors for a Nonautonomous Retarded Degenerate Parabolic Equation
Discrete Dynamics in Nature and Society, 2020 This paper is devoted to a nonautonomous retarded degenerate parabolic equation. We first show the existence and uniqueness of a weak solution for the equation by using the standard Galerkin method.
Fahe Miao, Hui Liu, Jie Xin
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Continuous maximal regularity on singular manifolds and its applications [PDF]
, 2015 In this article, we set up the continuous maximal regularity theory for a class of linear differential operators on manifolds with singularities. These operators exhibit degenerate or singular behaviors while approaching the singular ends.
Shao, Yuanzhen
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Fundamental solutions for degenerate parabolic equations [PDF]
Acta Mathematica, 1974 This chapter explains the construction of a candidate for a fundamental solution and the existence, smoothness, and certain bounds for a fundamental solution Γ. The underlying assumptions were that ( a ij , ( x )) is uniformly positive definite and a ij , b i are bounded and uniformly Holder continuous. The chapter presents a proof of how if a ij ,
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The cost of controlling strongly degenerate parabolic equations [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2020 We consider the typical one-dimensional strongly degenerate parabolic operator Pu = ut − (xαux)x with 0 < x < ℓ and α ∈ (0, 2), controlled either by a boundary control acting at x = ℓ, or by a locally distributed control. Our main goal is to study the dependence of the so-called controllability cost needed to drive an initial condition to rest ...
P. Cannarsa +2 more
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A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion [PDF]
Annales de l'Institut Henri Poincare. Analyse non linéar, 2022 The taxis-type migration-consumption model accounting for signal-dependent motilities, as given by ( u t = ∆ ( ) is considered for suitably smooth functions φ : [0 , ∞ ) → R which are such that φ > 0 on (0 , ∞ ), but that in addition φ (0) = 0 with φ ...
M. Winkler
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Asymptotic expansions for degenerate parabolic equations
Comptes Rendus. Mathématique, 2014 Abstract We prove asymptotic convergence results for some analytical expansions of solutions to degenerate PDEs with applications to financial mathematics. In particular, we combine short-time and global-in-space error estimates, previously obtained in the uniformly parabolic case, with some a priori bounds on “short cylinders”, and we achieve short ...
PASCUCCI, ANDREA +2 more
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