Results 41 to 50 of about 1,355,996 (330)

Admissible conditions for parabolic equations degenerating at infinity [PDF]

St. Petersburg Mathematical Journal, 2008
From the introduction: We investigate existence and uniqueness for bounded solutions of the parabolic Cauchy problem \[ \begin{aligned} \rho\partial_tu= \Delta u\quad &\text{in }\mathbb{R}^n\times \mathbb{R}_+:= S,\\ u= u_0\quad &\text{in }\mathbb{R}^n\times \{0\}\;(n\geq 3).\end{aligned}\tag{1.1} \] Concerning the coefficient \(\rho= \rho(x)\) and the
KAMIN S, POZIO, Maria Assunta, TESEI, Alberto   +2 more
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Finite element multistep multideriavative schemes for parabolic equations [PDF]

, 1976
The linear, homogeneous, parabolic equation is solved by applying finite element discretizations in space and A0 —stable, linear multistep, multiderivative (L.M.S.D.) methods in time. Such schemes are unconditionally stable. An error analysis establishes
Moore, P
core   +6 more sources

On the Weak Characteristic Function Method for a Degenerate Parabolic Equation

Journal of Function Spaces, 2019
For a nonlinear degenerate parabolic equation, how to impose a suitable boundary value condition to ensure the well-posedness of weak solutions is a very important problem.
Huashui Zhan
doaj   +1 more source

Degenerate singular parabolic problems with natural growth [PDF]

Opuscula Mathematica
In this paper, we study the existence and regularity results for nonlinear singular parabolic problems with a natural growth gradient term \[\begin{cases}\frac{\partial u}{\partial t}-\operatorname{div}((a(x,t)+u^{q})|\nabla u|^{p-2}\nabla u)+d(x,t)\frac{
Mounim El Ouardy, Youssef El Hadfi, Abdelaaziz Sbai   +2 more
doaj   +1 more source

Expansion of positivity to a class of doubly nonlinear parabolic equations

Electronic Journal of Qualitative Theory of Differential Equations, 2022
We establish the expansion of positivity of the nonnegative, local, weak solutions to the class of doubly nonlinear parabolic equations $$\partial_t (u^{q}) -\operatorname{div}{(|D u|^{p-2} D u)}=0, \qquad\ p>1 \ \text{and} \ q>0$$ considering ...
Eurica Henriques
doaj   +1 more source

Null controllability of one dimensional degenerate parabolic equations with first order terms [PDF]

Discrete & Continuous Dynamical Systems - B, 2019
In this paper we present a null controllability result for a degenerate semilinear parabolic equation with first order terms. The main result is obtained after the proof of a new Carleman inequality for a degenerate linear parabolic equation with first ...
J. Flores, L. de Teresa
semanticscholar   +1 more source

Singularly perturbed periodic parabolic equations with alternating boundary layer type solutions

Abstract and Applied Analysis, 2006
We consider a class of singularly perturbed parabolic equations for which the degenerate equations obtained by setting the small parameter equal to zero are algebraic equations that have several roots.
Adelaida B. Vasil'eva, Leonid V. Kalachev   +1 more
doaj   +2 more sources

The cost of controlling strongly degenerate parabolic equations [PDF]

E S A I M: Control, Optimisation and Calculus of Variations, 2018
We consider the typical one-dimensional strongly degenerate parabolic operator Pu = ut − (xαux)x with 0 < x < ℓ and α ∈ (0, 2), controlled either by a boundary control acting at x = ℓ, or by a locally distributed control.
P. Cannarsa, P. Martinez, J. Vancostenoble   +2 more
semanticscholar   +1 more source

The regular free boundary in the thin obstacle problem for degenerate parabolic equations [PDF]

St. Petersburg Mathematical Journal, 2019
In this paper we study the existence, the optimal regularity of solutions, and the regularity of the free boundary near the so-called \emph{regular points} in a thin obstacle problem that arises as the local extension of the obstacle problem for the ...
Agnid Banerjee, D. Danielli, N. Garofalo, A. Petrosyan   +3 more
semanticscholar   +1 more source

Stability for degenerate parabolic equations [PDF]

Advances in Calculus of Variations, 2010
The authors study the stability of the solutions of the evolutionary \(p\)-Laplace equation \[ {\partial u\over\partial t}= \nabla\cdot(|\nabla u|^{p-2}\nabla u) \] under variations of the parameter \(p\). The problem is delicate, since the underlying Sobolev space varieties with \(p\). The boundary values are given on the parabolic boundary of a space-
Parviainen, Mikko, Kinnunen, Juha
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