Results 21 to 30 of about 191 (49)

System of degenerate parabolic p-Laplacian

Open Mathematics
In this article, we study the mathematical properties of the solution u=(u1,…,uk){\bf{u}}=({u}^{1},\ldots ,{u}^{k}) to the degenerate parabolic system ut=∇⋅(∣∇u∣p−2∇u),(p>2).{{\bf{u}}}_{t}=\nabla \hspace{0.25em}\cdot \hspace{0.25em}({| \nabla {\bf{u}}| }^
Kim Sunghoon, Lee Ki-Ahm
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A free boundary model for transport-induced neurite growth

European Journal of Applied Mathematics
We introduce a free boundary model to study the effect of vesicle transport onto neurite growth. It consists of systems of drift-diffusion equations describing the evolution of the density of antero- and retrograde vesicles in each neurite coupled to ...
Greta Marino, Jan-Frederik Pietschmann, Max Winkler   +2 more
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Generalized result on the global existence of positive solutions for a parabolic reaction-diffusion model with an m × m diffusion matrix

Demonstratio Mathematica
The aim of this work is to study the global existence in time of solutions for the tridiagonal system of reaction-diffusion by order mm. Our techniques of proof are based on compact semigroup methods and some L1{L}^{1}-estimates.
Barrouk Nabila, Abdelmalek Karima
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Existence of global-in-time solutions to a system of fully nonlinear parabolic equations [PDF]

arXiv, 2022
We consider the Cauchy problem for a system of fully nonlinear parabolic equations. In this paper, we shall show the existence of global-in-time solutions to the problem. Our condition to ensure the global existence is specific to the fully nonlinear parabolic system.
arxiv  

Generation of semigroups associated to strongly coupled elliptic operator in $L^p(\mathbb R^d;\mathbb R^m)$ [PDF]

arXiv, 2022
A class of vector-valued elliptic operators with unbounded coefficients, coupled up to the second-order is investigated in the Lebesgue space $L^p(\mathbb R^d;\mathbb R^m)$ with $p \in (1,\infty)$, providing sufficient conditions for the generation of an analytic $C_0$-semigroup $T(t)$. Under further assumptions, a characterization of the domain of the
arxiv  

Deforming convex hypersurfaces to a hypersurface with prescribed harmonic mean curvature [PDF]

Science in China Ser A, 42(10), 1059-1066, (1999), 2003
A heat flow method is used to deform convex hypersurfaces in a ring domain to a hypersurface whose harmonic mean curvature is a prescribed function.
arxiv  

Strongly coupled Schroedinger operators in L^p(R^d;C^m) [PDF]

arXiv, 2023
We consider systems of elliptic equations, possibly coupled up to the second-order, on the L^p(R^d;C^m)-scale. Under suitable assumptions we prove that the minimal realization in L^p(R^d;C^m)$ generates a strongly continuous analytic semigroup. We also prove the consistency of the semigroup on the L^p-scale and some spectral results.
arxiv  

Stochastic Lagrangian Transport and Generalized Relative Entropies [PDF]

Commun. Math. Sci. 4 (2006), no. 4, 767--777, 2006
We discuss stochastic representations of advection diffusion equations with variable diffusivity, stochastic integrals of motion and generalized relative entropies.
arxiv  

Weak solutions of fractional differential equations in non cylindrical domain [PDF]

arXiv, 2016
We study a time fractional heat equation in a noncylindrical domain. The problem is one-dimensional. We prove existence of properly defined weak solutions by means of the Galerkin approximation.
arxiv  

Existence of global solutions to reaction-diffusion systems with nonhomogeneous boundary conditions via a Lyapunov functional

Electronic Journal of Differential Equations, 2002
Most publications on reaction-diffusion systems of $m$ components ($mgeq 2$) impose $m$ inequalities to the reaction terms, to prove existence of global solutions (see Martin and Pierre [10 ] and Hollis [4]).
Said Kouachi
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