A new kind of backward stochastic differential equations (in short BSDE), where the solution is a pair of processes adapted to the past of the driving Brownian motion, has been introduced by the authors in [63. It was then shown in a series of papers by the second and both authors (see [8, 7, 9, 103), that this kind of backward SDEs gives a probabilistic representation for the solution of a lar...

For scalar conservation laws posed on bounded domains in Rd, the convergence of quasilinear parabolic viscous approximations to entropy solution sense Bardos-Leroux-Nedelec is established.

In this paper we prove uniqueness in the inverse boundary value problem for three coefficient functions porous medium equation with an absorption term , space dimension 2 or higher. This is a degenerate parabolic type quasilinear PDE which has been used as model phenomena fields such gas flow (through medium), plasma physics, and population dynamics. case when priori, unique identifiability dat...

We present a new nonlinear version of the well-known Black-Scholes model for option pricing in financial mathematics. The partial differential equation is based on quasilinear diffusion term with p-Laplace operator \(\Delta_p\) \(1 < p \infty\). existence and uniqueness weak solution weighted Sobolev space proved, first, by methods parabolic problems using Gel'fand triplet and, alternatively...

By using the theory of maximal \begin{document}$ L^{q} $\end{document}-regularity and methods singular analysis, we show a Taylor's type expansion–with respect to geodesic distance around an arbitrary point–for solutions quasilinear parabolic equations on closed manifolds. The powers expansion are determi...