Generalized result on the global existence of positive solutions for a parabolic reaction diffusion model with a full diffusion matrix [PDF]
, 2023 In this paper, we study the global existence in time of solutions for a parabolic reaction diffusion model with a full matrix of diffusion coefficients on a bounded domain. The technique used is based on compact semigroup methods and some estimates.
Nabila Barrouk +3 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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Higher integrability for anisotropic parabolic systems of p-Laplace type
Advances in Nonlinear Analysis, 2023 In this article, we consider anisotropic parabolic systems of pp-Laplace type. The model case is the parabolic pi{p}_{i}-Laplace system ut−∑i=1n∂∂xi(∣Diu∣pi−2Diu)=0{u}_{t}-\mathop{\sum }\limits_{i=1}^{n}\frac{\partial }{\partial {x}_{i}}({| {D}_{i}u| }^{{
Mons Leon
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On oscillatory second order nonlinear impulsive systems of neutral type [PDF]
, 2020 In this work, the necessary and sufficient conditions for oscillation of a class of second order neutral impulsive systems are established and our impulse satisfies a discrete neutral nonlinear equation of similar type.
TRIPATHY, Arun Kumar +1 more
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Maximum principles for parabolic systems coupled in both first‐order and zero‐order terms
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 813-816, 1994., 1993 Some generalized maximum principles are established for linear second‐order parabolic systems in which both first‐order and zero‐order terms are coupled.
Chiping Zhou
wiley +1 more source
Unstable periodic wave solutions of Nerve Axion diffusion equations
International Journal of Mathematics and Mathematical Sciences, Volume 10, Issue 4, Page 787-796, 1987., 1987 Unstable periodic solutions of systems of parabolic equations are studied. Special attention is given to the existence and stability of solutions.
Rina Ling
wiley +1 more source
Exact Controllability of nonlinear Heat equations in spaces of analytic functions
, 2020 International audienceIt is by now well known that the use of Carleman estimates allows to establish the control-lability to trajectories of nonlinear parabolic equations.
Laurent, Camille, Rosier, Lionel
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The higher integrability of weak solutions of porous medium systems
Advances in Nonlinear Analysis, 2018 In this paper we establish that the gradient of weak solutions to porous medium-type systems admits the self-improving property of higher integrability.
Bögelein Verena +3 more
doaj +1 more source
Invariant Regions and Global Existence of Uniqueness Weak Solutions for Tridiagonal Reaction-Diffusion Systems [PDF]
In this paper we study the existence of uniqueness global weak solutions for m × m reaction-diffusion systems for which two main properties hold: the positivity of the weak solutions and the total mass of the components are preserved with time. Moreover,
BARROUK, Nabila +2 more
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System of degenerate parabolic p-Laplacian
Open MathematicsIn 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
doaj +1 more source