Search results for "Compensated compactness"

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A PDE model for the spatial dynamics of a voles population structured in age

2020

Abstract We prove existence and stability of entropy weak solutions for a macroscopic PDE model for the spatial dynamics of a population of voles structured in age. The model consists of a scalar PDE depending on time, t , age, a , and space x = ( x 1 , x 2 ) , supplemented with a non-local boundary condition at a = 0 . The flux is linear with constant coefficient in the age direction but contains a non-local term in the space directions. Also, the equation contains a term of second order in the space variables only. Existence of solutions is established by compensated compactness, see Panov (2009), and we prove stability by a doubling of variables type argument.

Parabolic–hyperbolic equationEnergy estimateseducation.field_of_studyConstant coefficientsDoubling of variablesPopulation dynamics structured in age and spaceApplied Mathematics010102 general mathematicsPopulationMathematical analysis01 natural sciences010101 applied mathematicsCompact spaceNon-local fluxCompensated compactnessPopulation dynamics structured in age and space Parabolic–hyperbolic equation Non-local flux Boundary value problem Energy estimates Compensated compactness Doubling of variablesBoundary value problem0101 mathematicseducationBoundary value problemAnalysisMathematics
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