Asymptotic behavior of the growth-fragmentation equation with bounded fragmentation rate
نویسندگان
چکیده
منابع مشابه
The asymptotic behavior of fragmentation processes
The fragmentation processes considered in this work are self-similar Markov processes which are meant to describe the ranked sequence of the masses of the pieces of an object that falls apart randomly as time passes. We investigate their behavior as t → ∞. Roughly, we show that the rate of decay of the ℓ p-norm (where p > 1) is exponential when the index of self-similarity α is 0, polynomial wh...
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Growth-fragmentation equations arise in many different contexts, ranging from cell division, protein polymerization, neurosciences etc. Direct observation of temporal dynamics being often difficult, it is of main interest to develop theoretical and numerical methods to recover reaction rates and parameters of the equation from indirect observation of the solution. Following the work done in Per...
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The discrete case of the growth-fragmentation equation is not as popular in the literature as the continuous form of it, hence the need to explore the discrete version of this model for some interesting analysis. In this paper, We examine the discrete growth-fragmentation equations. The problem is treated as an infinite-dimensional differential equation, posed in a suitable Banach space. Pertur...
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We study the kinetics of nonlinear irreversible fragmentation. Here fragmentation is induced by interactions/collisions between pairs of particles, and modelled by general classes of interaction kernels, and for several types of breakage models. We construct initial value and scaling solutions of the fragmentation equations, and apply the ”non-vanishing mass flux ”criterion for the occurrence o...
متن کاملEstimating the division rate and kernel in the fragmentation equation
We consider the fragmentation equation ∂f ∂t (t, x) = −B(x)f(t, x) + ∫ y=∞ y=x k(y, x)B(y)f(t, y)dy, and address the question of estimating the fragmentation parameters i.e. the division rate B(x) and the fragmentation kernel k(y, x) from measurements of the size distribution f(t, ·) at various times. This is a natural question for any application where the sizes of the particles are measured e...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2017
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2017.01.009