On global existence for semilinear parabolic systems

By Joakim Petersson. 2005

156 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/d77f6c5e5094873fd3d652ec428179ba5e1520d3

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Exponential decay toward equilibrium via entropy methods for reaction–diffusion equations (2006, background): “Moreover, we emphasize [20,21,34] for how generalized Lyapunov structures of reaction–diffusion systems yield a priori estimates to establish global existence of solutions.”
Monotone Dynamical Systems (2013, unknown): “For basic theory and further information on many topics we refer the reader to books of Amann [11], Henry [61] Cholewa and Dlotko [26], Hess [62], Lunardi [121] and Martin [122], the papers of Amann [7, 8, 9, 10], and the survey article of Poláčik [159].”
Positive steady states for a prey-predator model with some nonlinear diffusion terms (2006, background): “It should be noted that some prey–predator models with the linear diffusion terms have been extensively studied by many mathematicians: For example, see [2,6–8,17–21,30, 36] for the same reaction term in (P), and [3,9,26,28] for the Holling–Tanner reaction term case.”
Radial Solutions and Phase Separation in a System of Two Coupled Schrödinger Equations (2008, unknown): “By Lemma 2.6, {(u, u) : u ∈ Wr, u ≥ 0} ∩ A1 = ∅, which implies that A1 = B+ ∪ B− with disjoint subsets B± defined by B+ = {(u, v) ∈ A∗ : u ≥ v, u− v 6≡ 0}, B− = {(u, v) ∈ A∗ : u ≤ v, u− v 6≡ 0}.”
Global Existence in Reaction-Diffusion Systems with Control of Mass: a Survey (2010, methodology): “We refer to [49, 50, 24] for results in this direction.”
Quasi-steady-state approximation for a reaction–diffusion system with fast intermediate (2010, methodology): “We first prove here that global classical solutions do exist by adapting the L-duality technique developed in [19], [22], [23], [14].”