[图书][B] Superlinear parabolic problems

P Quittner, P Souplet - 2019 - Springer
Pavol Quittner Philippe Souplet Blow-up, Global Existence and Steady States Second
Edition Page 1 Birkhäuser Advanced Texts Basler Lehrbücher Pavol Quittner Philippe …

[HTML][HTML] Global and blow-up solutions for compressible Euler equations with time-dependent damping

S Chen, H Li, J Li, M Mei, K Zhang - Journal of Differential Equations, 2020 - Elsevier
This paper deals with the Cauchy problem for the compressible Euler equations with time-
dependent damping, where the time-vanishing damping in the form of μ (1+ t) λ makes some …

The stationary Gierer–Meinhardt system in the upper half-space: existence, nonexistence and asymptotics

M Ghergu - Mathematische Annalen, 2024 - Springer
We study the existence, nonexistence and asymptotics of positive solutions to the Gierer–
Meinhardt system-Δ u+ λ u= upvq+ ρ (x), u> 0 in R+ N:= RN-1×(0,∞),-Δ v+ λ v= umvs, v> 0 in …

[HTML][HTML] Steady state solutions for the Gierer-Meinhardt system in the whole space

M Ghergu - Journal of Differential Equations, 2023 - Elsevier
We are concerned with the study of positive solutions to the Gierer-Meinhardt system {− Δ u+
λ u= upv q+ ρ (x) in RN, N≥ 3,− Δ v+ μ v= umvs in RN, which satisfy u (x), v (x)→ 0 as …

[PDF][PDF] Existence, nonexistence and uniqueness of positive stationary solutions of a singular Gierer-Meinhardt system

R Peng, X Song, L Wei - Disc. Cont. Dyn. Syst, 2017 - researchgate.net
R d (d≥ 1) is a bounded smooth domain. New sufficient conditions, some of which are
necessary, on the existence of classical solutions are established. A uniqueness result of …

Global existence and blowup solutions for the Gierer–Meinhardt system

S Chen, B Melnick, R Xu - Nonlinear Analysis, 2020 - Elsevier
We discuss global and blowup solutions for general Gierer–Meinhardt system with zero
Neumann boundary conditions, which originally arose in studies of pattern-formation in …

Blow-up of positive solutions to a singular Gierer–Meinhardt system

S Chen, R Xu - Nonlinear Analysis: Real World Applications, 2019 - Elsevier
This paper deals with blow-up of positive solutions for a singular Gierer–Meinhardt system
subject to zero Dirichlet boundary conditions. We first prove the existence of a local solution …

[HTML][HTML] The explicit solution to the initial–boundary value problem of Gierer–Meinhardt model

X An, Z He, X Song - Applied Mathematics Letters, 2018 - Elsevier
Using the solutions of an elliptic system and an ODE system, under certain conditions, we
get the explicit solution to the following initial–boundary value problem of Gierer-Meinhardt …

[HTML][HTML] Bounded solutions to a singular parabolic system

S Chen, Y Salmaniw, R Xu - Journal of Mathematical Analysis and …, 2017 - Elsevier
In this paper, we are concerned with the singular parabolic system ut= Δ u+ f (x) v− p, vt= Δ
v+ g (x) u− q in a smooth bounded domain Ω⊂ RN subject to zero Dirichlet conditions, with …

[HTML][HTML] Uniformly bounded weak and classical solutions to a singular parabolic system and applications

Y Salmaniw - Journal of Mathematical Analysis and Applications, 2020 - Elsevier
Equations of both elliptic and parabolic type featuring singular nonlinearities have appeared
in numerous works throughout the years. In this work, we consider a time dependent …