We consider the Cauchy problem related to the partial differential equation Lu = Δxu + h(u)∂yu - ∂ tu = f(·, u), where (x,y,t) ∈ ℝN × ℝ ×]0,T[, which arises in mathematical finance and in the theory oi diffusion processes. We study the regularity of solutions regarding L as a perturbation of an operator of Kolmogorov type. We prove the existence of local classical solutions and give some sufficient conditions for global existence.
Pascucci, A., Polidoro, S. (2004). On the cauchy problem for a nonlinear Kolmogorov equation. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 35(3), 579-595 [10.1137/S0036141001399349].
On the cauchy problem for a nonlinear Kolmogorov equation
PASCUCCI, ANDREA;
2004
Abstract
We consider the Cauchy problem related to the partial differential equation Lu = Δxu + h(u)∂yu - ∂ tu = f(·, u), where (x,y,t) ∈ ℝN × ℝ ×]0,T[, which arises in mathematical finance and in the theory oi diffusion processes. We study the regularity of solutions regarding L as a perturbation of an operator of Kolmogorov type. We prove the existence of local classical solutions and give some sufficient conditions for global existence.File in questo prodotto:
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