On a modified parabolic complex Monge–Ampère equation with applications

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

The geometric properties of a degenerate parabolic equation with periodic source term

In this paper, we discuss the geometric properties of solution and lower bound estimate of ∆um−1 of the Cauchy problem for a degenerate parabolic equation with periodic source term ut =∆um+ upsint. Our objective is to show that: (1)with continuous variation of time t, the surface ϕ = [u(x,t)]mδq is a complete Riemannian manifold floating in space RN+1and is tangent to the space RN at ∂H0(t); (2...

a quasilinear parabolic equation with inhomogeneous density and absorption

Weak Solution of Parabolic Complex Monge-ampère Equation

We study the equation u̇ = log det(uαβ̄)−Au+f(z, t) in domains of C. This equation has a close connection with the Kähler-Ricci flow. In this paper, we consider the case where the boundary condition is smooth and the initial condition is irregular.

A Nonlinear Parabolic - Sobolev Equation

Let M and I, be (nonlinear) operators in a reflexive Banach space B for which Rg(M + L) = B and j(Mx My) i~(Lx Ly)( > / Mx My / for all 01 > 0 and pairs s, y in D(M) n D(L). Then there is a unique solution of the Cauchy problem (Mu(t))’ + Lu(t) = 0, Mu(O) = v0 . When M and L are realizations of elliptic partial differential operators in space variables, this gives existence and uniqueness of ge...