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Weak solutions and supersolutions in L 1 for reaction-diffusion systems
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In this article, it was shown that the limits of nonnegative solutions to reaction-diffusion systems whose nonlinearities are bounded in L^1 time converges to supersolutions of the system.Abstract:
We prove here that limits of nonnegative solutions to reaction-diffusion systems whose nonlinearities are bounded in \( L^1 \) always converge to supersolutions of the system. The motivation comes from the question of global existence in time of solutions for the wide class of systems preserving positivity and for which the total mass of the solution is uniformly bounded. We prove that, for a large subclass of these systems, weak solutions exist globally.read more
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Superlinear Parabolic Problems: Blow-up, Global Existence and Steady States
Pavol Quittner,Philippe Souplet +1 more
TL;DR: In this article, the authors propose a model for solving the model elliptic problems and model parabolic problems. But their model is based on Equations with Gradient Terms (EGS).
Journal ArticleDOI
Global Existence in Reaction-Diffusion Systems with Control of Mass: a Survey
TL;DR: In this article, the authors describe the state of the art on the question of global existence of solutions to reaction-diffusion systems for which two main properties hold: on one hand, the positivity of the solutions is preserved for all time; on the other hand the total mass of the components is uniformly controlled in time.
Journal ArticleDOI
Global existence for quadratic systems of reaction-diffusion
TL;DR: In this article, the authors prove global existence in time of weak solutions to a class of quadratic reaction-diffusion systems for which a Lyapounov structure of LlogL-entropy type holds.
Journal ArticleDOI
Improved Duality Estimates and Applications to Reaction-Diffusion Equations
TL;DR: For general systems in any space dimension, this article obtained smooth solutions of reaction-diffusion systems coming out of reversible chemistry under the assumption that the diffusion coefficients are sufficiently close one to another.
Journal ArticleDOI
Global Existence of Renormalized Solutions to Entropy-Dissipating Reaction–Diffusion Systems
TL;DR: In this article, the authors introduce the notion of a renormalized solution for reaction-diffusion systems with entropy-dissipating reactions and establish the global existence of such solutions.
References
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Linear and Quasilinear Equations of Parabolic Type
TL;DR: In this article, the authors considered a hyperbolic parabolic singular perturbation problem for a quasilinear equation of kirchhoff type and obtained parameter dependent time decay estimates of the difference between the solutions of the solution of a quasi-linear parabolic equation and the corresponding linear parabolic equations.
Journal ArticleDOI
Semi-linear second-order elliptic equations in L1
Haim Brezis,Walter A. Strauss +1 more
Journal Article
Semi-linear second-order elliptic equations in L 1
Haim Brezis,Walter A. Strauss +1 more
Journal ArticleDOI
Sublinear elliptic equations in ℝn
Haim Brezis,Shoshana Kamin +1 more
TL;DR: In this paper, the strong maximum principle was used to show that if such a solution exists, then u > 0 in in, then n > 3 with 0 0, p not identically zero.