2,641 research outputs found
A unified existence theory for evolution equations and systems under nonlocal conditions
We investigate the effect of nonlocal conditions expressed by linear
continuous mappings over the hypotheses which guarantee the existence of global
mild solutions for functional-differential equations in a Banach space. A
progressive transition from the Volterra integral operator associated to the
Cauchy problem, to Fredholm type operators appears when the support of the
nonlocal condition increases from zero to the entire interval of the problem.
The results are extended to systems of equations in a such way that the system
nonlinearities behave independently as much as possible and the support of the
nonlocal condition may differ from one variable to another.Comment: 19 page
The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials
This paper is concerned with the analysis of the Cauchy problem of a general
class of two-dimensional nonlinear nonlocal wave equations governing anti-plane
shear motions in nonlocal elasticity. The nonlocal nature of the problem is
reflected by a convolution integral in the space variables. The Fourier
transform of the convolution kernel is nonnegative and satisfies a certain
growth condition at infinity. For initial data in Sobolev spaces,
conditions for global existence or finite time blow-up of the solutions of the
Cauchy problem are established.Comment: 15 pages. "Section 6 The Anisotropic Case" added and minor changes.
Accepted for publication in Nonlinearit
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