Results 1 to 10 of about 193 (162)

Quasilinear Parabolic Equations Associated with Semilinear Parabolic Equations

Mathematics, 2023
We formulate a quasilinear parabolic equation describing the behavior of the global-in-time solution to a semilinear parabolic equation. We study this equation in accordance with the blow-up and quenching patterns of the solution to the original ...
Katsuyuki Ishii, Michel Pierre, Takashi Suzuki   +2 more
doaj   +3 more sources

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 \(s\geq 0\), \((n-1)/(n+1)n(1-m)-1-m-2s.\)
Yuan-Wei Qi
exaly   +3 more sources

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 ...
Fabio Cipriani, Gabriele Grillo
exaly   +4 more sources

Monotone economical schemes for quasilinear parabolic equations

Mathematical Modelling and Analysis, 2002
In order to approximate a multidimensional quasilinear parabolic equation with unlimited nonlinearity the economical vector‐additive scheme is constructed.
N. V. Dzenisenko, A. P. Matus, P. P. Matus   +2 more
doaj   +4 more sources

Nonlinear parabolic equation having nonstandard growth condition with respect to the gradient and variable exponent [PDF]

Opuscula Mathematica, 2021
We are concerned with the existence of solutions to a class of quasilinear parabolic equations having critical growth nonlinearity with respect to the gradient and variable exponent.
Abderrahim Charkaoui, Houda Fahim, Nour Eddine Alaa   +2 more
doaj   +1 more source

Constrained Evolution for a Quasilinear Parabolic Equation [PDF]

Journal of Optimization Theory and Applications, 2016
Key words: feedback control, quasilinear parabolic equation, monotone nonlinearities, convex ...
Colli, Pierluigi, Gilardi, Gianni, Sprekels, Jürgen   +2 more
openaire   +6 more sources

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

On Comparison Principles for Parabolic Equations with Nonlocal Boundary Conditions

Boundary Value Problems, 2007
A generalization of the comparison principle for a semilinear and a quasilinear parabolic equations with nonlocal boundary conditions including changing sign kernels is obtained.
Yuandi Wang, Hamdi Zorgati
doaj   +2 more sources

On the local integrability and boundedness of solutions to quasilinear parabolic systems

Electronic Journal of Qualitative Theory of Differential Equations, 2004
We introduce a structure condition of parabolic type, which allows for the generalization to quasilinear parabolic systems of the known results of integrability, and boundedness of local solutions to singular and degenerate quasilinear parabolic ...
T. Giorgi, M. O'Leary
doaj   +1 more source

Classical and weak solutions of the partial differential equations associated with a class of two-point boundary value problems

Boundary Value Problems, 2018
This paper is concerned with a kind of first-order quasilinear parabolic partial differential equations associated with a class of ordinary differential equations with two-point boundary value problems. We prove that the function given by the solution of
Ning Ma, Zhen Wu
doaj   +1 more source