Highly nonlinear large-competition limits of elliptic systems

DOI10.1016/j.na.2010.05.008zbMath1196.35215OpenAlexW2075986318MaRDI QIDQ984111

Elaine C. M. Crooks, E. Norman Dancer

Publication date: 13 July 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.05.008

zbMATH Keywords

singular limitsspatial segregationcompetition systemsquadratic gradient growth

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) A priori estimates in context of PDEs (35B45) Theoretical approximation in context of PDEs (35A35) Semilinear elliptic equations (35J61) Boundary value problems for second-order elliptic systems (35J57)

Related Items (7)

Non-variational weakly coupled elliptic systems ⋮ Asymptotic behavior of positive solutions to a predator-prey elliptic system with strong hunting cooperation in predators ⋮ Ground states of nonlinear Schrödinger systems with mixed couplings ⋮ Infinitely many nonradial positive solutions for multi-species nonlinear Schrödinger systems in \(\mathbb{R}^N\) ⋮ Uniform Hölder bounds for a strongly coupled elliptic system with strong competition ⋮ Spatial segregation limit of a non-autonomous competition-diffusion system ⋮ The spatial behavior of a strongly coupled non-autonomous elliptic system

Cites Work

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• Calcium waves with fast buffers and mechanical effects
• Competing species equations with diffusion, large interactions, and jumping nonlinearities
• Dynamics of Lotka-Volterra competition systems with large interaction
• An optimal partition problem related to nonlinear eigenvalues.
• Fast reaction limit and long time behavior for a competition-diffusion system with Dirichlet boundary conditions
• On the long term spatial segregation for a competition-diffusion system
• Invariant criteria for existence of solutions to second-order quasilinear elliptic equations
• Traveling Waves in Buffered Systems: Applications to Calcium Waves

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