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math.CA2017★ 1 cited
A Discontinuous Differential Calculus in the Framework Colombeau's Full Algebra
Wagner Cortes, Antonio R. G. Garcia, Severino H. da Silva
Starting from the Colombeau's full generalized functions, the sharp topologies and the notion of generalized points, we introduce a new kind differential calculus (for functions be…
math.DS2017
Dissipative property for a class of non local evolution equations
Severino H. da Silva, Antonio R. G. Garcia, Bruna E. P. Lucena
In this work we consider the non local evolution problem \[ \begin{cases} \partial_t u(x,t)=-u(x,t)+g(βK(f\circ u)(x,t)+βh), ~x \inΩ, ~t\in[0,\infty[;\\ u(x,t)=0, ~x\in\mathbb{R}^N…