Existence of Local Solutions to a Class of Doubly Degenerate Parabolic Equations

This paper deals with a class of doubly degenerate parabolic equations, including as particular cases the porous medium equation and the degenerate pLaplace equation （p 〉 2）ut-div（b（x,t,u）｜↓△u｜^p-2↓△u）=f（x,u,t）The initial-boundary value problem in a bounded domain of R^N is considered under mixed boundary conditions. The existence of local-in-time weak solutions is obtained.

Blow Up for Solutions of Nonlinear Doubly Degenerate Parabolic Equation

This paper studies the conditions of blow up in finite time of solutions of initial boundary value problem for a class nonlinear doubly degenerate parabolic equation.

Doubly Degenerate Parabolic Equation with Nonlinear Inner and Boundary Sources

This paper deals with blow-up criterion for a doubly degenerate parabolic equation of the form （u^n）t = （｜ux｜^m-1ux）x ＋ u^p in （0, 1） × （0,T） subject to nonlinear boundary source （｜ux｜^m-1ux）（1,t） = u^q（1,t）, （｜ux｜^m-1ux）（0,t） = O, and positive initial data u（x,0） = uo（x）, where the parameters va, n, p, q 〉0. It is proved that the problem possesses global solutions if and only if p ≤ n and q〈min {n,m（n＋1）/m＋1}.

Blow-up for Doubly Degenerate Nonlinear Parabolic Equations

In this paper, we give a complete picture of the blow-up criteria for weak solutions of the Dirichlet problem of some doubly degenerate nonlinear parabolic equations.

INITIAL TRACE OF SOLUTIONS FOR A DOUBLY NONLINEAR DEGENERATE PARABOLIC EQUATIONS

In this note, we study the existence of an initial trace of nonnegative solutions for the following problem ut-div（｜▽um｜p-2^▽um）＋uq = 0 in QT = Ω × （0, T ）. We prove that the initial trace is an outer regular Borel measure, which may not be locally bounded for some values of parameters p, q, and m. We also study the corresponding Cauchy problems with a given generalized Borel measure as initial data.

FINITE SPEED OF PROPAGATION OF SOLUTIONS FOR SOME QUASILINEAR HIGHER ORDER PARABOLIC EQUATIONS WITH DOUBLY STRONG DEGENERATION

Under some conditions, one seows that the generalized solutions of the first boundary value problem for the equation [GRAPHICS] have the property of finite speed of propagation.

Extinction and Positivity for a Doubly Nonlinear Degenerate Parabolic Equation

The aims of this paper are to discuss the extinction and positivity for the solution of the initial boundary value problem and Cauchy problem of ut = div（[↓△u^m｜p-2↓△u^m）. It is proved that the weak solution will be extinct for 1 〈 p ≤ 1 ＋ 1/m and will be positive for p 〉 1 ＋ 1/m for large t, where m 〉 0.

Doubly Nonlinear Degenerate Parabolic Equations with a Singular Potential for Greiner Vector Fields

The purpose of this paper is to investigate the nonexistence of positive so lutions of the following doubly nonlinear degenerate parabolic equations:{∂u=▽k·(u^(m-1)|▽ku|^(p-2)▽ku)+(w)u^(m+p-2),u(w,0)=u0(w)≥0,u(w,t)=0,inΩ×(0,T),inΩ,on∂Ω×(0,T),where Q is a Carnot-Carathéodory metric bal in IR^(2n+1)generated by Greiner vector fields,V∈L_(loc)(Ω),k∈N,m∈R,1<p<2n+2k and m+p-2>0.The better lower bound p*for m+p is found and the nonexistence results are proved for p*≤m+p<3.