On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient
Electronic Journal of Differential Equations, 2002 We study the Cauchy problem for the nonlinear (possibly strongly) degenerate parabolic transport-diffusion equation $$ partial_t u + partial_x (gamma(x)f(u))=partial_x^2 A(u), quad A'(cdot)ge 0, $$ where the coefficient $gamma(x)$ is possibly ...
John D. Towers +2 more
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Blow-up for an evolution
Boundary Value Problems, 2011 This paper investigates the blow-up properties of positive solutions to the following system of evolution p-Laplace equations with nonlocal sources and inner absorptions { u t − div ( | ∇ u | p − 2 ∇ u ) =
Liu Dengming +3 more
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Convergence rate for the incompressible limit of nonlinear diffusion–advection equations [PDF]
Annales de l'Institut Henri Poincare. Analyse non linéar, 2021 The incompressible limit of nonlinear diffusion equations of porous medium type has attracted a lot of attention in recent years, due to its ability to link the weak formulation of cell-population models to free boundary problems of Hele-Shaw type ...
Noemi David, Tomasz Dkebiec, B. Perthame
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On the logarithmic type boundary modulus of continuity for the Stefan problem [PDF]
Advances in Mathematics, 2021 A logarithmic type modulus of continuity is established for weak solutions to a two-phase Stefan problem, up to the parabolic boundary of a cylindrical space-time domain.
Naian Liao
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Diffusion–convection reaction equations with sign-changing diffusivity and bistable reaction term [PDF]
Nonlinear Analysis: Real World Applications, 2021 We consider a reaction-diffusion equation with a convection term in one space variable, where the diffusion changes sign from the positive to the negative and the reaction term is bistable.
Diego Berti, A. Corli, L. Malaguti
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On the fine properties of parabolic measures associated to strongly degenerate parabolic operators of Kolmogorov type [PDF]
Advances in Mathematics, 2020 We consider strongly degenerate parabolic operators of the form L := ∇X · (A(X,Y, t)∇X) +X · ∇Y − ∂t in unbounded domains Ω = {(X,Y, t) = (x, xm, y, ym, t) ∈ R m−1 × R× R × R× R | xm > ψ(x, y, t)}.
M. Litsgaard, K. Nystrom
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Global attractors for a class of semilinear degenerate parabolic equations
Open Mathematics, 2021 In this paper, we consider the long-time behavior for a class of semi-linear degenerate parabolic equations with the nonlinearity ff satisfying the polynomial growth of arbitrary p−1p-1 order.
Zhu Kaixuan, Xie Yongqin
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Blow-up results of the positive solution for a class of degenerate parabolic equations
Open Mathematics, 2021 This paper is devoted to discussing the blow-up problem of the positive solution of the following degenerate parabolic equations: (r(u))t=div(∣∇u∣p∇u)+f(x,t,u,∣∇u∣2),(x,t)∈D×(0,T∗),∂u∂ν+σu=0,(x,t)∈∂D×(0,T∗),u(x,0)=u0(x),x∈D¯.\left\{\begin{array}{ll}{(r ...
Dong Chenyu, Ding Juntang
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Saturated Fronts in Crowds Dynamics
Advanced Nonlinear Studies, 2021 We consider a degenerate scalar parabolic equation, in one spatial dimension, of flux-saturated type. The equation also contains a convective term. We study the existence and regularity of traveling-wave solutions; in particular we show that they can be ...
Campos Juan +2 more
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Properties of generalized degenerate parabolic systems
Advances in Nonlinear Analysis, 2022 In this article, we consider the parabolic system (ui)t=∇⋅(mUm−1A(∇ui,ui,x,t)+ℬ(ui,x,t)),(1≤i≤k){({u}^{i})}_{t}=\nabla \cdot (m{U}^{m-1}{\mathcal{A}}(\nabla {u}^{i},{u}^{i},x,t)+{\mathcal{ {\mathcal B} }}({u}^{i},x,t)),\hspace{1.0em}(1\le i\le k) in the ...
Kim Sunghoon, Lee Ki-Ahm
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