Local existence and uniqueness of solutions of a degenerate parabolic system

On Uniqueness and Existence of Entropy Solutions of Weakly Coupled Systems of Nonlinear Degenerate Parabolic Equations

We prove existence and uniqueness of entropy solutions for the Cauchy problem of weakly coupled systems of nonlinear degenerate parabolic equations. We prove existence of an entropy solution by demonstrating that the Engquist-Osher finite difference scheme is convergent and that any limit function satisfies the entropy condition. The convergence proof is based on deriving a series of a priori e...

Existence and Uniqueness of Weak Solutions to Parabolic IVP’s

= −divax, t∇u + b⃗x, t ⋅ ∇u + cx, tux, t with aij, bj, c ∈ LUT and for a0 > 0, z⃗ ⋅ aijx, t z⃗ ≥ a0 | z⃗| ∀z⃗ ∀x, t ∈ UT. Then L is said to be uniformly elliptic on UT. We recall that the assumptions on the coefficients aij, bj, c, imply the existence of positive constants, a1,a0 and μ0 such that for all u,v ∈ H1U, and μ > μ0, |Bu,v, t| ≤ a1‖u‖1‖v‖1 a.e. t ∈ 0,T Bu,u, t +...

Existence and Nonexistence of Global Solutions of Some Non-local Degenerate Parabolic Systems

This paper establishes a new criterion for global existence and nonexistence of positive solutions of the non-local degenerate parabolic system ut = v p ( ∆u+ a ∫

Existence of Solutions for Degenerate Parabolic Equations with Rough Coefficients

We prove that a sequence of quasi-solutions to non-degenerate degenerate parabolic equations with rough coefficients is strongly Lloc-precompact. The result is obtained using the H-measures and a new concept of quasihomogeneity. A consequence of the precompactness is existence of a weak solution to the equation under consideration.

Global existence of solutions to a parabolic-elliptic chemotaxis system with critical degenerate di ffusion