On a class of fully nonlinear parabolic equations
Advances in Nonlinear Analysis, 2016 We study the homogeneous Dirichlet problem for the fully nonlinear ...
Antontsev Stanislav, Shmarev Sergey
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Behavior of different numerical schemes for population genetic drift problems [PDF]
, 2016 In this paper, we focus on numerical methods for the genetic drift problems, which is governed by a degenerated convection-dominated parabolic equation.
Chen, Minxin +4 more
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Stabilization of arbitrary structures in a three-dimensional doubly degenerate nutrient taxis system
European Journal of Applied MathematicsThe doubly degenerate nutrient taxis system (0.1) \begin{equation} \left \{ \begin{aligned} &u_{t}=\nabla \cdot (uv\nabla u)-\chi \nabla \cdot (u^{\alpha }v\nabla v)+\ell uv,&x\in \Omega ,\, t\gt 0,\\[5pt] & v_{t}=\Delta v-uv,&x\in \Omega ,\, t\gt 0,\\
Xiang-Mao De-Ji, Ai Huang, Yifu Wang
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Interior Estimates for Generalized Forchheimer Flows of Slightly Compressible Fluids
Advanced Nonlinear Studies, 2017 The generalized Forchheimer flows are studied for slightly compressible fluids in porous media with time-dependent Dirichlet boundary data for the pressure. No restrictions are imposed on the degree of the Forchheimer polynomial. We derive, for all time,
Hoang Luan T., Kieu Thinh T.
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Ireneo Peral: Forty Years as Mentor
Advanced Nonlinear Studies, 2017 In this article we present a survey of the Ph.D. theses that have been completed under the advice of Ireneo Peral.Following a chronological order, we summarize the main results contained in the works of the former students of Ireneo Peral.
Abdellaoui Boumediene +9 more
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Continuity of the temperature in a multi-phase transition problem. [PDF]
Math Ann, 2022 Gianazza U, Liao N.
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Harnack's inequality for doubly nonlinear equations of slow diffusion type. [PDF]
Calc Var Partial Differ Equ, 2021 Bögelein V +3 more
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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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A degenerate migration-consumption model in domains of arbitrary dimension
Advanced Nonlinear StudiesIn a smoothly bounded convex domain Ω⊂Rn ${\Omega}\subset {\mathbb{R}}^{n}$ with n ≥ 1, a no-flux initial-boundary value problem forut=Δuϕ(v),vt=Δv−uv, $$\begin{cases}_{t}={\Delta}\left(u\phi \left(v\right)\right),\quad \hfill \\ {v}_{t}={\Delta}v-uv ...
Winkler Michael
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Existence of solutions to a diffusive shallow medium equation. [PDF]
J Evol Equ, 2021 Bögelein V, Dietrich N, Vestberg M.
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