14,502 research outputs found
A 3-dimensional singular kernel problem in viscoelasticity: an existence result
Materials with memory, namely those materials whose mechanical and/or
thermodynamical behaviour depends on time not only via the present time, but
also through its past history, are considered. Specifically, a three
dimensional viscoelastic body is studied. Its mechanical behaviour is described
via an integro-differential equation, whose kernel represents the relaxation
modulus, characteristic of the viscoelastic material under investigation.
According to the classical model, to guarantee the thermodynamical
compatibility of the model itself, such a kernel satisfies regularity
conditions which include the integrability of its time derivative. To adapt the
model to a wider class of materials, this condition is relaxed; that is,
conversely to what is generally assumed, no integrability condition is imposed
on the time derivative of the relaxation modulus. Hence, the case of a
relaxation modulus which is unbounded at the initial time t = 0, is considered,
so that a singular kernel integro-differential equation, is studied. In this
framework, the existence of a weak solution is proved in the case of a three
dimensional singular kernel initial boundary value problem.Comment: 15 page
Non-negative solutions of systems of ODEs with coupled boundary conditions
We provide a new existence theory of multiple positive solutions valid for a wide class of
systems of boundary value problems that possess a coupling in the boundary conditions.
Our conditions are fairly general and cover a large number of situations. The theory is illustrated
in details in an example. The approach relies on classical fixed point index
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