Results 11 to 20 of about 1,312 (223)
ON THE GLOBAL EXISTENCE OF SOLUTIONS TO QUASILINEAR PARABOLIC EQUATIONS [PDF]
Glasgow Mathematical Journal, 2004 The subject of the paper is the following quasilinear parabolic problem (P): \[ u_t - \text{div\,} (a(t,x,u) \nabla u) = f(t,x,u, \nabla u) \qquad \text{for} \quad t>0, \; x \in \Omega, \] \[ u(t,x) = 0 \quad \text{for} \quad t>0, \; x \in \partial \Omega, \qquad u(0,x) = \varphi (x) \quad \text{for} \quad x \in \bar \Omega.
Yin, Zhaoyang,, Lund University.
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Boundary Value Problems, 2020 The aim of this paper is to show some applications of Sobolev inequalities in partial differential equations. With the aid of some well-known inequalities, we derive the existence of global solution for the quasilinear parabolic equations.
Yuanfei Li, Lianhong Guo, Peng Zeng
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Flow relaxation method in solving quasilinear parabolic equations [PDF]
Компьютерные исследования и моделирование, 2011 This article proposes a numeric method of solution of quasilinear parabolic equations, based on the flux approximation, describes the implementation of the method on a rectangular grid and presents numerical results.
Alexey I. Lobanov, V. A. Usenko
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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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Quasilinear Evolution Equations in LμP-Spaces with Lower Regular Initial Data
Journal of Function Spaces, 2018 We study the Cauchy problem of the quasilinear evolution equations in Lμp-spaces. Based on the theories of maximal Lp-regularity of sectorial operators, interpolation spaces, and time-weighted Lp-spaces, we establish the local posedness for a class of ...
Qinghua Zhang
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Nonlinear second order evolution equations with state-dependent delays
Electronic Journal of Qualitative Theory of Differential Equations, 2012 We consider second order quasilinear parabolic equations where also the main part contains functional dependence and state-dependent delay on the unknown function. Existence and some qualitative properties of the solutions are shown.
László Simon
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On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation [PDF]
Discrete Dynamics in Nature and Society, 2009 By Oleinik′s line method, we study the existence and the uniqueness of the classical solution of the Cauchy problem for the following equation in [0, T] × R2: ∂xxu + u∂yu − ∂tu = f(⋅, u), provided that T is suitable small. Results of numerical experiments are reported to demonstrate that the strong solutions of the above equation may blow up in ...
Zongqi Liang, Huashui Zhan
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Weak solutions to a multi-phase field system of parabolic equations related to alloy solidification [PDF]
, 2007 Existence of weak solutions to a phase field model for solidification of alloys is studied. The model consists of balance equations for the energy and the concentrations of the alloy components which are coupled to a system of Allen-Cahn equations ...
Stinner, Björn
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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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Global solutions for quasilinear parabolic problems
, 2002 Results on the global existence of classical solutions for quasilinear parabolic equations in bounded domains with homogeneous Dirichlet or Neumann boundary conditions are presented.
Constantin, Adrian, +2 more
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