5,546 research outputs found
Convergence of Rothe scheme for hemivariational inequalities of parabolic type
This article presents the convergence analysis of a sequence of piecewise
constant and piecewise linear functions obtained by the Rothe method to the
solution of the first order evolution partial differential inclusion
, where the multivalued term
is given by the Clarke subdifferential of a locally Lipschitz functional. The
method provides the proof of existence of solutions alternative to the ones
known in literature and together with any method for underlying elliptic
problem, can serve as the effective tool to approximate the solution
numerically. Presented approach puts into the unified framework known results
for multivalued nonmonotone source term and boundary conditions, and
generalizes them to the case where the multivalued term is defined on the
arbitrary reflexive Banach space as long as appropriate conditions are
satisfied. In addition the results on improved convergence as well as the
numerical examples are presented.Comment: to appear in: International Journal of Numerical Analysis and
Modelin
Global attractors for multivalued semiflows with weak continuity properties
A method is proposed to deal with some multivalued semiflows with weak
continuity properties. An application to the reaction-diffusion problems with
nonmonotone multivalued semilinear boundary condition and nonmonotone
multivalued semilinear source term is presented.Comment: to appear in Nonlinear Analysis Series A, Theory, Methods &
Application
Modified Einstein's gravity to probe the sub- and super-Chandrasekhar limiting mass white dwarfs: a new perspective to unify under- and over-luminous type Ia supernovae
Type Ia supernovae (SNeIa), used as one of the standard candles in
astrophysics, are believed to form when the mass of the white dwarf approaches
Chandrasekhar mass limit. However, observations in last few decades detected
some peculiar SNeIa, which are predicted to be originating from white dwarfs of
mass much less than the Chandrasekhar mass limit or much higher than it.
Although the unification of these two sub-classes of SNeIa was attempted
earlier by our group, in this work, we, for the first time, explain this
phenomenon in terms of just one property of the white dwarf which is its
central density. Thereby we do not vary the fundamental parameters of the
underlying gravity model in the contrary to the earlier attempt. We effectively
consider higher order corrections to the Starobinsky- gravity model to
reveal the unification. We show that the limiting mass of a white dwarf is
for central density g/cc, while it
is for g/cc under the same
model parameters. We further confirm that these models are viable with respect
to the solar system test. This perhaps enlightens very strongly the long
standing puzzle lying with the predicted variation of progenitor mass in SNeIa.Comment: 15 pages including 6 figures: published in JCA
On non-autonomously forced Burgers equation with periodic and Dirichlet boundary conditions
We study the non-autonomously forced Burgers equation
on the space interval with two sets of the boundary conditions:
the Dirichlet and periodic ones. For both situations we prove that there exists
the unique bounded trajectory of this equation defined for all . Moreover we demonstrate that this trajectory attracts all
trajectories both in pullback and forward sense. We also prove that for the
Dirichlet case this attraction is exponential
Attractors for Navier-Stokes flows with multivalued and nonmonotone subdifferential boundary conditions
We consider two-dimensional nonstationary Navier-Stokes shear flow with
multivalued and nonmonotone boundary conditions on a part of the boundary of
the flow domain. We prove the existence of global in time solutions of the
considered problem which is governed by a partial differential inclusion with a
multivalued term in the form of Clarke subdifferential. Then we prove the
existence of a trajectory attractor and a weak global attractor for the
associated multivalued semiflow. This research is motivated by control problems
for fluid flows in domains with semipermeable walls and membranes.Comment: A correction was introduced in assertion (ii) of Definition 4.4 and -
accordingly - in the proof of Theorem 4.
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