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Blow-up Estimates of the Positive Solution of a Parabolic System
This paper establishes the blow-up estimates for the systems ut − Δu = 0, vt − Δv = 0 in BR × (0, T), BR ⊂ Rn, with the nonlinear boundary conditions ∂u∂η=um1vn1 and ∂v∂η=um2vn2 on SR × (0, T) whereExpand
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Blow-up analysis for a system of heat equations coupled through a nonlinear boundary condition
We show that the blow-up rate of the system of heat equations uit − Δui = 0 (i = 1,…, k, uk+1 ≔ u1) in Ω × (0,T) coupled through nonlinear boundary conditions ∂u i ∂η = u p i i+1 is proportional to the blowup rate. Expand
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Coupled diffusion systems with localized nonlinear reactions
This paper deals with the blowup rate and profile near the blowup time for the system of diffusion equations uit − Δui = upii+1(x0, t), (i = 1, …, k, uk+1 := u1) in Ω × (0, T) with boundaryExpand
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Instability induced by cross-diffusion in reaction–diffusion systems
Abstract In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficient conditions forExpand
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Stability patterns for a size-structured population model and its stage-structured counterpart.
In this paper we compare a general size-structured population model, where a size-structured consumer feeds upon an unstructured resource, to its simplified stage-structured counterpart in terms ofExpand
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Boundary Control of Linear Evolution PDEs - Continuous and Discrete
Consider a partial differential equation (PDE) of evolution type, such as the wave equation or the heat equation. Assume now that you can influence the behavior of the solution by setting theExpand
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Stability in a diffusive food-chain model with Michaelis–Menten functional response
Abstract This paper deals with the behavior of positive solutions to a reaction–diffusion system with homogeneous Neumann boundary conditions describing a three species food chain. A sufficientExpand
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Functional Analysis in Applied Mathematics and Engineering
Topological and Metric Spaces Banach Spaces Bounded Operators Hilbert Spaces Operators in Hilbert Space Spectral Theory Integral Operators Semigroups of Evolution Sobolev Spaces Interpolation SpacesExpand
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Well-posedness of inverse problems for systems with time dependent parameters
In this paper we investigate the abstract hyperbolic model with time dependent stiffness and damping given by 〈u(t), ψ〉V ∗,V + d(t; u(t), ψ) + a(t;u(t), ψ) = 〈f(t), ψ〉V ∗,V where V ⊂ VD ⊂ H ⊂ V ∗ D ⊂Expand
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Periodicity and blowup in a two-species cooperating model
Abstract In this paper, the cooperating two-species Lotka–Volterra model is discussed. The existence and asymptotic behavior of T -periodic solutions for the periodic reaction diffusion system underExpand
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