Results 11 to 20 of about 420,318 (376)
On the local integrability and boundedness of solutions to quasilinear parabolic systems [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2004 We introduce a structure condition of parabolic type, which allows for the generalization to quasilinear parabolic systems of the known results of integrability, and boundedness of local solutions to singular and degenerate quasilinear parabolic ...
Giorgi, T., O'Leary, M.
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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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Multiplicative controllability for nonlinear degenerate parabolic equations between sign-changing states [PDF]
E S A I M: Control, Optimisation and Calculus of Variations, 2020 In this paper we study the global approximate multiplicative controllability for nonlinear degenerate parabolic Cauchy problems. In particular, we consider a one-dimensional semilinear degenerate reaction-diffusion equation in divergence form governed ...
Floridia, Giuseppe +2 more
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Hölder gradient estimates for a class of singular or degenerate parabolic equations [PDF]
Advances in Nonlinear Analysis, 2017 We prove interior Hölder estimates for the spatial gradients of the viscosity solutions to the singular or degenerate parabolic ...
Imbert Cyril +2 more
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Gaussian bounds for degenerate parabolic equations
Journal of Functional Analysis, 2008 AbstractLet A be a real symmetric, degenerate elliptic matrix whose degeneracy is controlled by a weight w in the A2 or QC class. We show that there is a heat kernel Wt(x,y) associated to the parabolic equation wut=divA∇u, and Wt satisfies classic Gaussian bounds:|Wt(x,y)|⩽C1tn/2exp(−C2|x−y|2t).
David Cruz-Uribe, Cristian Rios
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Degenerate semilinear parabolic equations [PDF]
Differential and Integral Equations, 1992 Andreas Stahel
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Fujita-type results for the degenerate parabolic equations on the Heisenberg groups [PDF]
Nonlinear Differential Equations and Applications NoDEA, 2023 In this paper, we consider the Cauchy problem for the degenerate parabolic equations on the Heisenberg groups with power law non-linearities. We obtain Fujita-type critical exponents, which depend on the homogeneous dimension of the Heisenberg groups ...
A. Fino, Michael Ruzhansky, B. Torebek
semanticscholar +1 more source
An energy formula for fully nonlinear degenerate parabolic equations in one spatial dimension [PDF]
Mathematische Annalen, 2022 Energy (or Lyapunov) functions are used to prove stability of equilibria, or to indicate a gradient-like structure of a dynamical system. Matano constructed a Lyapunov function for quasilinear non-degenerate parabolic equations. We modify Matano's method
Phillipo Lappicy, Ester Beatriz
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Regularity results for a class of widely degenerate parabolic equations [PDF]
Advances in Calculus of Variations, 2022 Motivated by applications to gas filtration problems, we study the regularity of weak solutions to the strongly degenerate parabolic PDE u t - div ( ( | D u | - ν ) + p - 1 D u | D u | ) = f in Ω T = Ω × ( 0 , T ) , u_{t}-\operatorname{div}\
Pasquale Ambrosio +1 more
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The Wolff gradient bound for degenerate parabolic equations
Journal of the European Mathematical Society, 2014 The spatial gradient of solutions to non-homogeneous and degenerate parabolic equations of p -Laplacean type can be pointwise estimated by natural Wolff potentials of the right hand side measure.
Mingione, Giuseppe, Kuusi, Tuomo
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