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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Computing optimal control with a quasilinear parabolic partial differential equation [PDF]
Surveys in Mathematics and its Applications, 2009 This paper presents the numerical solution of a constrained optimal control problem (COCP) for quasilinear parabolic equations. The COCP is converted to unconstrained optimization problem (UOCP) by applying the exterior penalty function method. Necessary
M. H. Farag
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On qualitative properties of a system containing a singular parabolic functional equation [PDF]
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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Blow-Up Analysis for a Quasilinear Parabolic Equation with Inner Absorption and Nonlinear Neumann Boundary Condition [PDF]
Abstract and Applied Analysis, 2014 We investigate an initial-boundary value problem for a quasilinear parabolic equation with inner absorption and nonlinear Neumann boundary condition. We establish, respectively, the conditions on nonlinearity to guarantee that u(x,t) exists globally or ...
Zhong Bo Fang, Yan Chai
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Existence of solutions for quasilinear parabolic equations with nonlocal boundary conditions
Electronic Journal of Differential Equations, 2011 We prove the existence of a generalized solution a quasilinear parabolic equation with nonlocal boundary conditions, using the Faedo-Galerkin approximation.
Baili Chen
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Existence and Nonexistence of Global Solutions of the Quasilinear Parabolic Equations with Inhomogeneous Terms [PDF]
Advances in Difference Equations, 2010 We consider the quasilinear parabolic equation with inhomogeneous term , , where , , , , and , . In this paper, we investigate the critical exponents of this equation.
Kobayashi Yasumaro
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Steady-state solutions of a mass-conserving bistable equation with a saturating flux [PDF]
, 2012 We consider a mass-conserving bistable equation with a saturating flux on an interval. This is the quasilinear analogue of the Rubinstein–Steinberg equation, suitable for description of order parameter conserving solid–solid phase transitions in the case
Grinfeld, Michael +3 more
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Well-posedness and stationary solutions [PDF]
, 2011 In this paper we prove existence and uniqueness of variational inequality solutions for a bistable quasilinear parabolic equation arising in the theory of solid-solid phase transitions and discuss its stationary solutions, which can be ...
Grinfeld, Michael, Burns, Martin
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Large time behavior in a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system [PDF]
, 2022 summary:This paper deals with a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system. Boundedness, stabilization and blow-up in this system of the fully parabolic and parabolic-elliptic-elliptic versions have already been ...
Chiyo, Yutaro +2 more
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Finite-difference method for the Gamma equation on non-uniform grids
Vietnam Journal of Science, Technology and Engineering, 2022 We propose a new monotone finite-difference scheme for the second-order local approximation on a nonuniform grid that approximates the Dirichlet initial boundary value problem (IBVP) for the quasi-linear convection-diffusion equation with unbounded ...
Le Minh Hieu +2 more
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