On the existence of a solution of the Laplace equation with a nonlinear dynamic boundary conditionстатья
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Дата последнего поиска статьи во внешних источниках: 28 мая 2015 г.
Местоположение издательства:Road Town, United Kingdom
Первая страница:92
Последняя страница:107
Аннотация:The authors derive from the concrete Maxwell's equations in a medium and study the following very interesting evolutionary problem that includes the stationary Laplace equation in a half-plane and nonlinear boundary conditions containing a derivative in time:
Δu=0, x3>0, t>0,
(∂2u∂t∂x3+∂u∂x3+|u|qu)∣∣∣x3=0=0, x′=(x1,x2)∈R2, t>0,
u(x′,0)=u0(x′), x′∈R2.
They reduce this problem to a system of nonlinear integral equations and then obtain several results on the existence and nonexistence of a global solution to this problem.