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The applications of Sobolev inequalities in proving the existence of solution of the quasilinear parabolic equation [PDF]

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
doaj   +2 more sources

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, Michel Pierre, Takashi Suzuki   +2 more
doaj   +3 more sources

Quasilinear Evolution Equations and Parabolic Systems [PDF]

Transactions of the American Mathematical Society, 1986
It is shown that general quasilinear parabolic systems possess unique maximal classical solutions for sufficiently smooth initial values, provided the boundary conditions are “time-independent”. Moreover it is shown that, in the autonomous case, these equations generate local semiflows on appropriate Sobolev spaces. Our results apply, in particular, to
Herbert Amann
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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, A. P. Matus, P. P. Matus   +2 more
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Stability of solutions of quasilinear parabolic equations [PDF]

Journal of Mathematical Analysis and Applications, 2003
17 ...
Giuseppe Maria Coclite, Helge Holden
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Locally Invariant Manifolds for Quasilinear Parabolic Equations [PDF]

Rocky Mountain Journal of Mathematics, 1991
The paper is concerned with the geometric study of an evolution equation of the form \(x'-Lx=f(t,\lambda,x)\), where \(L:D(L)\to X\) is the generator of a holomorphic semigroup and the nonlinearity \(f\) acts essentially from some interpolation space \(D_ L(\theta+1)\) to \(D_ L(\theta)\).
Alexander Mielke
openalex   +3 more sources

Existence and Nonexistence of Global Solutions of the Quasilinear Parabolic Equations with Inhomogeneous Terms

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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Global and blowup solutions of quasilinear parabolic equation with critical Sobolev exponent and lower energy initial value

Journal of Inequalities and Applications, 2001
In this paper, by means of the energy method, we first study the existence and asymptotic estimates of global solution of quasilinear parabolic equations involving -Laplacian and critical Sobolev exponent and lower energy initial value in a bounded ...
Yao Zheng-An, Tan Zhong
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Nonlinear parabolic equation having nonstandard growth condition with respect to the gradient and variable exponent [PDF]

Opuscula Mathematica, 2021
We are concerned with the existence of solutions to a class of quasilinear parabolic equations having critical growth nonlinearity with respect to the gradient and variable exponent.
Abderrahim Charkaoui, Houda Fahim, Nour Eddine Alaa   +2 more
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Critical Fujita exponents for a class of quasilinear coupled parabolic equations

Electronic Journal of Differential Equations
Yuanyuan Nie, Yan Leng, Xu Zhao, Qian Zhou   +3 more
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