Displaying similar documents to “Well Posedness of Balance Laws with Non-Characteristic Boundary”

Symmetric hyperbolic systems with boundary conditions that do not satisfy the Kreiss-Sakamoto condition

Matthias Eller (2008)

Applicationes Mathematicae

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Symmetric hyperbolic systems with a class of non-homogeneous boundary conditions that do not satisfy the Kreiss-Sakamoto condition (or uniform Lopatinskii condition) are discussed. The boundary conditions are of conservative type. An energy estimate which provides interior and boundary regularity for weak solutions to the system is proved. The results are valid for operators with rough coefficients. As an example the anisotropic Maxwell system is considered.

Positive solutions with given slope of a nonlocal second order boundary value problem with sign changing nonlinearities

P. Ch. Tsamatos (2004)

Annales Polonici Mathematici

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We study a nonlocal boundary value problem for the equation x''(t) + f(t,x(t),x'(t)) = 0, t ∈ [0,1]. By applying fixed point theorems on appropriate cones, we prove that this boundary value problem admits positive solutions with slope in a given annulus. It is remarkable that we do not assume f≥0. Here the sign of the function f may change.