Results 1 to 10 of about 953 (219)
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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Journal of Function Spaces, 2021 This paper deals with a class of quasilinear parabolic equation with power nonlinearity and nonlocal source under homogeneous Dirichlet boundary condition in a smooth bounded domain; we obtain the blow-up condition and blow-up results under the condition
Xiaorong Zhang, Zhoujin Cui
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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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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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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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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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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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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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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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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.
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