On a comparison theorem for parabolic equations with nonlinear boundary conditions
Advances in Nonlinear Analysis, 2022 In this article, a new type of comparison theorem for some second-order nonlinear parabolic systems with nonlinear boundary conditions is given, which can cover classical linear boundary conditions, such as the homogeneous Dirichlet or Neumann boundary ...
Kita Kosuke, Ôtani Mitsuharu
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An inertial manifold and the principle of spatial averaging
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 5, Page 293-299, 2001., 2001 We examine the existence of inertial manifold of a class of differential equations with particular boundary conditions.
Hyukjin Kwean
wiley +1 more source
On the lifespan of classical solutions to a non-local porous medium problem with nonlinear boundary conditions [PDF]
, 2019 In this paper we analyze the porous medium equation \begin{equation}\label{ProblemAbstract} \tag{$\Diamond$} %\begin{cases} u_t=\Delta u^m + a\io u^p-b u^q -c\lvert\nabla\sqrt{u}\rvert^2 \quad \textrm{in}\quad \Omega \times I,%\\ %u_\nu-g(u)=0 & \textrm ...
Marras, Monica +2 more
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Large Time Behaviour of the Solution of a Nonlinear Diffusion Problem in Anthropology
Journal of Mathematical Study, 2018 In this article we consider a reaction-diffusion model for the spreading of farmers in Europe, which was occupied by hunter-gatherers; this process is known as the Neolithic agricultural revolution.
J. Eliaš
semanticscholar +1 more source
Local existence result of the single dopant diffusion including cluster reactions of high order
Abstract and Applied Analysis, Volume 6, Issue 1, Page 13-34, 2001., 2001 We consider the pair diffusion process which includes cluster reactions of high order. We are able to prove a local (in time) existence result in arbitrary space dimensions. The model includes a nonlinear system of reaction‐drift‐diffusion equations, a nonlinear system of ordinary differential equations in Banach spaces, and a nonlinear elliptic ...
R. Bader, W. Merz
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Traveling waves for the Keller–Segel system with Fisher birth terms
, 2008 We consider the traveling wave problem for the one dimensional Keller-Segel system with a birth term of either a Fisher/KPP type or with a truncation for small population densities. We prove that there exists a solution under some stability conditions on
Grégoire Nadin, B. Perthame, L. Ryzhik
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Attractors of multivalued semiflows generated by differential inclusions and their approximations
Abstract and Applied Analysis, Volume 5, Issue 1, Page 33-46, 2000., 2000 We prove the existence of global compact attractors for differential inclusions and obtain some results concerning the continuity and upper semicontinuity of the attractors for approximating and perturbed inclusions. Applications are given to a model of regional economic growth.
Alexei V. Kapustian, José Valero
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Front instability in a condensed phase combustion model
Advances in Nonlinear Analysis, 2015 We consider a condensed phase (or solid) combustion model and its linearization around the travelling front solution. We construct an Evans function to characterize the eigenvalues of the linearized problem.
Bonnet Alexis +2 more
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Existence and Multiplicity of Weak Solutions for a Neumann Elliptic Problem with -Laplacian
Nonautonomous Dynamical Systems, 2020 We are interested in the existence of multiple weak solutions for the Neumann elliptic problem involving the anisotropic -Laplacian operator, on a bounded domain with smooth boundary.
Bohner Martin +3 more
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Asymptotic behavior of type I blowup solutions to a parabolic-elliptic system of drift-diffusion type [PDF]
, 2010 A Cauchy problem for a parabolic-elliptic system of drift-di usion type is considered. The problem is formally of the form Ut = r (rU Ur( ) 1U): This system describes a mass-conserving aggregation phenomenon including gravitational collapse and ...
Noriko, Mizoguchi +2 more
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