A Quasilinear Parabolic Equation with Quadratic Growth of the Gradient modeling Incomplete Financial Markets

A Quasilinear Parabolic Equation with Quadratic Growth of the Gradient modeling Incomplete Financial Markets

We consider a quasilinear parabolic equation with quadratic gradient terms. It arises in the modelling of an optimal portfolio which maximizes the expected utility from terminal wealth in incomplete markets consisting of risky assets and non-tradable state variables. The existence of solutions is shown by extending the monotonicity method of Frehse. Furthermore, we prove the uniqueness of weak ...

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

Asymptotic Behavior of Solutions to a Degenerate Quasilinear Parabolic Equation with a Gradient Term

This article concerns the asymptotic behavior of solutions to the Cauchy problem of a degenerate quasilinear parabolic equations with a gradient term. A blow-up theorem of Fujita type is established and the critical Fujita exponent is formulated by the spacial dimension and the behavior of the coefficient of the gradient term at ∞.

a quasilinear parabolic equation with inhomogeneous density and absorption

Quenching Profile for a Quasilinear Parabolic Equation

where 00, Z>0, and uq(x) >0, Vx G [—1, Z]. Without loss of generality, we may assume that uq(x) is smooth and bounded above by 1 such that uo(±Z) = 1. Since uo(x) is positive, the local (in time) existence and uniqueness of a classical solution of the problem (1.1)—(1.3) are trivial (see [8]). Many results in quenching, such as single point quenching and profiles, are similar to those b...