We consider the Cauchy problem related to the partial differential equationLu ≡ Δ_x u + h(u)∂_y u − ∂_t u = f(·, u),where (x, y, t) ∈ R^N × R × ]0, T[, which arises in mathematical finance and in the theory of diffusion processes. We study the regularity of solutions regarding L as a perturbation of an operatorof Kolmogorov type. We prove the existence of local classical solutions and give some sufficient conditions for global existence.
On the Cauchy problem for a non linear Kolmogorov equation / Pascucci, A.; Polidoro, Sergio. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - 35,3:(2003), pp. 579-595.
On the Cauchy problem for a non linear Kolmogorov equation
POLIDORO, Sergio
2003
Abstract
We consider the Cauchy problem related to the partial differential equationLu ≡ Δ_x u + h(u)∂_y u − ∂_t u = f(·, u),where (x, y, t) ∈ R^N × R × ]0, T[, which arises in mathematical finance and in the theory of diffusion processes. We study the regularity of solutions regarding L as a perturbation of an operatorof Kolmogorov type. We prove the existence of local classical solutions and give some sufficient conditions for global existence.
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