Results 11 to 20 of about 12,675 (193)

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
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Extinction Phenomenon and Decay Estimate for a Quasilinear Parabolic Equation with a Nonlinear Source

Advances in Mathematical Physics, 2021
By energy estimate approach and the method of upper and lower solutions, we give the conditions on the occurrence of the extinction and nonextinction behaviors of the solutions for a quasilinear parabolic equation with nonlinear source.
Dengming Liu, Luo Yang
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Existence and smoothing effects of the initial-boundary value problem for \partial u/\partial t-\Delta\sigma(u)=0 in time-dependent domains [PDF]

Opuscula Mathematica, 2023
We show the existence, smoothing effects and decay properties of solutions to the initial-boundary value problem for a generalized porous medium type parabolic equations of the form \[u_t-\Delta \sigma(u) =0 \quad \text{in } Q(0, T)\] with the initial ...
Mitsuhiro Nakao
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The Existence and Behavior of Solutions for Nonlocal Boundary Problems

Boundary Value Problems, 2009
The purpose of this work is to investigate the uniqueness and existence of local solutions for the boundary value problem of a quasilinear parabolic equation. The result is obtained via the abstract theory of maximal regularity. Applications are given to
Shengzhou Zheng, Yuandi Wang
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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
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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
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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
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Quasilinear parabolic stochastic partial differential equations: existence, uniqueness [PDF]

, 2015
In this paper, we provide a direct approach to the existence and uniqueness of strong (in the probabilistic sense) and weak (in the PDE sense) solutions to quasilinear stochastic partial differential equations, which are neither monotone nor locally ...
Hofmanova, Martina, Zhang, Tusheng
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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
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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
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