Global solvability of an initial-boundary value problem for a semilinear system of equationsстатья
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Дата последнего поиска статьи во внешних источниках: 28 мая 2015 г.
Местоположение издательства:Road Town, United Kingdom
Первая страница:1000
Последняя страница:1011
Аннотация:The author considers the following system of PDEs supplied with initial data and arising in the theory of semiconductors:
∂tP+P+ε1|P|p1P=ΔP−∂φ∂x1,x=(x1,x2,x3)∈Ω, t>0,
Δφ−ε2|φ|p2φ=∂P∂x1,x∈Ω,
where εi are positive constants, Ω is a bounded domain with a smooth boundary and pi are subcritical exponents satisfying 0≤pi≤4. First, he proves the existence and uniqueness of a global weak solution of the system. Then, he shows the exponential decay of this solution as t goes to ∞. He also generalizes these results for other spatial dimensions.