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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회지 대한수학회지 제58권 제5호
- 발행연도
- 2021.9
- 수록면
- 1,109 - 1,129 (21page)
- DOI
- 10.4134/JKMS.j200369
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초록· 키워드
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This paper considers an anisotropic polytropic infiltration equation with a source term $$ {u_t}= \sum_{i=1}^N\frac{\partial }{\partial x_i}\left(a_i(x)|u|^{\alpha_i}{\left| {u_{x_i}} \right|^{p_i-2}}u_{x_i}\right)+f(x,t,u), $$ where $p_i>1$, $\alpha_i >0$, $a_i(x)\geq 0$. The existence of weak solution is proved by parabolically regularized method. Based on local integrability $u_{x_i}\in W^{1,p_i}_{loc}(\Omega)$, the stability of weak solutions is proved without boundary value condition by the weak characteristic function method. One of the essential characteristics of an anisotropic equation different from an isotropic equation is found originally.
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참고문헌 (24)
참고문헌 신청
D. Andreucci / 2001 / Large Time Behavior of Solutions to the Neumann Problem for a Quasilinear Second Order Degenerate Parabolic Equation in Domains with Noncompact Boundary / Journal of Differential Equations 174(2):253~288
S.N. Antontsev / 2005 / A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions / Nonlinear Analysis: Theory, Methods & Applications 60(3):515~545
Stanislav Antontsev / 2006 / Elliptic equations and systems with nonstandard growth conditions: Existence, uniqueness and localization properties of solutions / Nonlinear Analysis: Theory, Methods & Applications 65(4):728~761
Mostafa Bendahmane / 2003 / On some anisotropic reaction-diffusion systems with L1-data modeling the propagation of an epidemic disease / Nonlinear Analysis: Theory, Methods & Applications 54(4):617~636
C. S. Chen / 2001 / Global existence of and L1 estimates for solutions for a doubly degenerate parabolic equation / Acta Math. Sinica (Chin. Ser.) 44(6):1089~1098
S.N. Antontsev / 2005 / A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions / Nonlinear Analysis: Theory, Methods & Applications 60(3):515~545
Stanislav Antontsev / 2006 / Elliptic equations and systems with nonstandard growth conditions: Existence, uniqueness and localization properties of solutions / Nonlinear Analysis: Theory, Methods & Applications 65(4):728~761
Mostafa Bendahmane / 2003 / On some anisotropic reaction-diffusion systems with L1-data modeling the propagation of an epidemic disease / Nonlinear Analysis: Theory, Methods & Applications 54(4):617~636
C. S. Chen / 2001 / Global existence of and L1 estimates for solutions for a doubly degenerate parabolic equation / Acta Math. Sinica (Chin. Ser.) 44(6):1089~1098
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