Results 21 to 30 of about 1,295,553 (207)

On qualitative properties of a system containing a singular parabolic functional equation

Electronic Journal of Qualitative Theory of Differential Equations, 2008
We consider a system consisting of a quasilinear parabolic equation and a first order ordinary differential equation containing functional dependence on the unknown functions. The existence and some properties of solutions in $(0,\infty )$ will be proved.
László Simon
doaj   +1 more source

Existence and stability of traveling waves in parabolic systems of differential equations with weak diffusion

Karpatsʹkì Matematičnì Publìkacìï, 2022
The aim of the present paper is to investigate of some properties of periodic solutions of a nonlinear autonomous parabolic systems with a periodic condition.
I.I. Klevchuk
doaj   +1 more source

Critical Exponents of Quasilinear Parabolic Equations

Journal of Mathematical Analysis and Applications, 2002
The critical exponent for the global existence of positive solutions of the equation \[ u_t = \text{div}(|\nabla u|^{m-1}\nabla u)+t^s|x|^\sigma u^p \] in \(\mathbb R^n\) is found for \(s\geq 0\), \((n-1)/(n+1)n(1-m)-1-m-2s.\)
Qi, YW, Wang, MX
openaire   +2 more sources

Some results about an anisotropic -Laplace–Barenblatt equation

Advances in Nonlinear Analysis, 2012
We investigate the following quasilinear parabolic equation of Barenblatt type,
Giacomoni Jacques, Vallet Guy
doaj   +1 more source

Stability of solutions of quasilinear parabolic equations

Journal of Mathematical Analysis and Applications, 2005
We bound the difference between solutions $u$ and $v$ of $u_t = aΔu+\Div_x f+h$ and $v_t = bΔv+\Div_x g+k$ with initial data $ϕ$ and $ ψ$, respectively, by $\Vert u(t,\cdot)-v(t,\cdot)\Vert_{L^p(E)}\le A_E(t)\Vert ϕ-ψ\Vert_{L^\infty(\R^n)}^{2ρ_p}+ B(t)(\Vert a-b\Vert_{\infty}+ \Vert \nabla_x\cdot f-\nabla_x\cdot g\Vert_{\infty}+ \Vert f_u-g_u\Vert_ ...
COCLITE, Giuseppe Maria, HOLDEN H.
openaire   +3 more sources

A note on quasilinear parabolic equations on manifolds

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2012
We prove short time existence, uniqueness and continuous dependence on the initial data of smooth solutions of quasilinear locally parabolic equations of arbitrary even order on closed manifolds.
Mantegazza Carlo Maria, LUCA MARTINAZZI
openaire   +8 more sources

An H1-Galerkin method for a Stefan problem with a quasilinear parabolic equation in non-divergence form

International Journal of Mathematics and Mathematical Sciences, 1987
Optimal error estimates in L2, H1 and H2-norm are established for a single phase Stefan problem with quasilinear parabolic equation in non-divergence form by an H1-Galerkin procedure.
A. K. Pani, P. C. Das
doaj   +1 more source

Filtration in cohesive soils: numerical approach

Computer Assisted Methods in Engineering and Science, 2023
Paper presents a numerical method for solving the initial boundary-value problem for a certain quasilinear parabolic equation describing the low velocity filtration problem. The convergence of the method is proved.
Robert Schaefer, Stanislaw Sędziwy
doaj  

Uniform Bounds for Solutions to Quasilinear Parabolic Equations

Journal of Differential Equations, 2001
The authors consider a class of quasilinear parabolic equations on a domain \(D \subset \mathbb{R}^d\) of finite Lebesgue measure in the form \[ u_t(t,x) = \text{div\,} a(t,x,u(t,x), \nabla u(t,x)); \quad t \in (0,\infty),\;x \in D. \] where \(a : (0,\infty)\times D \times \mathbb{R} \times \mathbb{R}^d \to \mathbb{R}^d\) is a Carathéodory function ...
CIPRIANI, FABIO EUGENIO GIOVANNI, GRILLO, GABRIELE   +1 more
openaire   +3 more sources

On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification

Abstract and Applied Analysis, 2003
This paper deals with weak solution in weighted Sobolev spaces, of three-point boundary value problems which combine Dirichlet and integral conditions, for linear and quasilinear parabolic equations in a domain with curved lateral boundaries. We, firstly,
Abdelfatah Bouziani
doaj   +1 more source