Results 1 to 10 of about 12,446 (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 +2 more
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The quasilinear parabolic kirchhoff equation
Open Mathematics, 2017 In this paper the existence of solution of a quasilinear generalized Kirchhoff equation with initial – boundary conditions of Dirichlet type will be studied using the Leray – Schauder principle.
Dawidowski Łukasz
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Quasilinear parabolic stochastic partial differential equations: existence, uniqueness [PDF]
Stochastic Processes and their Applications, 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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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 +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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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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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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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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