On semidiscrete models dominated by the heat, wave and Laplace equations

Reaction-diffusion equations (35K57) Heat equation (35K05) Lattice dynamics and infinite-dimensional dissipative dynamical systems (37L60) Ordinary lattice differential equations (34A33) Lattice functional-differential equations (34K31) Functional-differential and differential-difference operators (47E07)

Cites Work

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Chaotic asymptotic behaviour of the solutions of the Lighthill-Whitham-Richards equation
Explicit solutions to dynamic diffusion-type equations and their time integrals
Dynamics of birth-and-death processes with proliferation -- stability and chaos
Dynamic diffusion-type equations on discrete-space domains
The SMM model as a boundary value problem using the discrete diffusion equation
Introduction to large truncated Toeplitz matrices
Heat kernel expansions on the integers
Hölder-Lebesgue regularity and almost periodicity for semidiscrete equations with a fractional Laplacian
Maximum principles for discrete and semidiscrete reaction-diffusion equation
Propagation failure of traveling waves in a discrete bistable medium
Exponential number of stationary solutions for Nagumo equations on graphs
On the spectrum of weighted shifts
Asymptotic behavior of solutions to the semidiscrete diffusion equation
Discrete advection-diffusion equations on graphs: maximum principle and finite volumes
Spatial dynamics for lattice differential equations with a shifting habitat
Invariant regions for systems of lattice reaction-diffusion equations
Harmonic analysis associated with a discrete Laplacian
Well-posedness and maximum principles for lattice reaction-diffusion equations
CHAOTIC ASYMPTOTIC BEHAVIOR OF THE HYPERBOLIC HEAT TRANSFER EQUATION SOLUTIONS
Vector-valued Laplace Transforms and Cauchy Problems
Asymptotic profile of solutions for the damped wave equation with a nonlinear convection term
TOPOLOGICAL CHAOS FOR A CLASS OF LINEAR MODELS
Transport equation on semidiscrete domains and Poisson–Bernoulli processes
Some simple differential difference equations and the related functions

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