Pricing multi-asset financial derivatives with time-dependent parameters -- Lie algebraic approach.
Qualitative properties of solutions to semilinear heat equations with singular initial data.
Quasi-linearisation methods for a nonlinear heat equation with functional dependence.
Quasilinearization methods for nonlinear differential-functional parabolic equations: unbounded case
We consider the Cauchy problem for nonlinear parabolic equations with functional dependence represented by the Hale functional acting on the unknown function and its gradient. We prove convergence theorems for a general quasilinearization method in natural subclasses of unbounded solutions.
Quasilinearization methods for nonlinear parabolic equations with functional dependence.
Regular self-similar solutions of the nonlinear heat equation with initial data above the singular steady state
Relaxation approximations and bounded variation estimates for some partial differential equations.
Renormalized solution for nonlinear degenerate problems in the whole space
We consider the general degenerate parabolic equation :We suppose that the flux is continuous, is nondecreasing continuous and both functions are not necessarily Lipschitz. We prove the existence of the renormalized solution of the associated Cauchy problem for initial data and source term. We establish the uniqueness of this type of solution under a structure condition and an assumption on the modulus of continuity of . The novelty of this work is that , , , , are not Lipschitz...
Scaling in nonlinear parabolic equations: locality versus globality
Schauder theorems for linear elliptic and parabolic problems with unbounded coefficients in
We study existence, uniqueness, and smoothing properties of the solutions to a class of linear second order elliptic and parabolic differential equations with unbounded coefficients in . The main results are global Schauder estimates, which hold in spite of the unboundedness of the coefficients.
Second order parabolic equations and weak uniqueness of diffusions with discontinuous coefficients
We prove the unique solvability of parabolic equations with discontinuous leading coefficients in . Using this result, we establish the uniqueness of diffusion processes with time-dependent discontinuous coefficients.
Self-similar singular solution of doubly singular parabolic equation with gradient absorption term.
Self-similar solutions for a nonlinear degenerate parabolic equation.
Semigroup theory applied to options.
Sets of admissible initial data for porous-medium equations with absorption.
Sharp asymptotic estimates for vorticity solutions of the 2D Navier-Stokes equation.
Singular solutions of doubly singular parabolic equations with absorption.
Solution entropique pour une équation parabolique-hyperbolique non linéaire
Solution généralisée locale d'une équation parabolique quasi linéaire dégénérée du second ordre
Solutions in Gevrey spaces of partial differential equations with constant coefficients
Si dà una condizione sufficiente per la esistenza di una soluzione in uno spazio di Gevrey , razionale , , di una equazione lineare a derivate parziali a coefficienti costanti , quando . La dimostrazione completa dei risultati ottenuti è contenuta in una nota dell’autore in corso di pubblicazione su "Astérisque".