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An Application Of The Theory Of Scale Of Banach Spaces

100%
Dawidowski Ł.
Annales Mathematicae Silesianae
|
2015
|
tom 29
|
nr 1
51-59
EN
The abstract Cauchy problem on scales of Banach space was considered by many authors. The goal of this paper is to show that the choice of the space on scale is significant. We prove a theorem that the selection of the spaces in which the Cauchy problem ut − Δu = u|u|s with initial–boundary conditions is considered has an influence on the selection of index s. For the Cauchy problem connected with the heat equation we will study how the change of the base space influents the regularity of the solutions.
2
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Analytical approximation of the transition density in a local volatility model

76%
Pagliarani S., Pascucci A.
Open Mathematics
|
2012
|
tom 10
|
nr 1
250-270
EN
We present a simplified approach to the analytical approximation of the transition density related to a general local volatility model. The methodology is sufficiently flexible to be extended to time-dependent coefficients, multi-dimensional stochastic volatility models, degenerate parabolic PDEs related to Asian options and also to include jumps.
3
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The finite speed of propagation of solutions of the Neumann problem of a degenerate parabolic equation

64%
Pan J.
Open Mathematics
|
2011
|
tom 9
|
nr 3
673-685
EN
In this paper the finite speed of propagation of solutions and the continuous dependence on the nonlinearity of a degenerate parabolic partial differential equation are discussed. Our objective is to derive an explicit expression for the speed of propagation and the large time behavior of the solution and to show that the solution continuously depends on the nonlinearity of the equation.
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