Existence and regularity results for a singular parabolic equations with degenerate coercivity

Ouardy, Mounim El; Hadfi, Youssef El; Ifzarne, Aziz

doi:10.3934/dcdss.2021012

Cited by 13 publications

(4 citation statements)

References 22 publications

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“…For the existence and regularity results to the anisotropic elliptic case of problem (1.1), we refer the reader to reference [31]. Finally, concerning the singular model case the authors in [26] studied existence and regularity of problem…”

Section: Introductionmentioning

confidence: 99%

Bounded Solutions for Anisotropic Degenerate Parabolic Problems with Singular Term

Zaater

Khelifi

2023

Preprint

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Note: Please see pdf for full abstract with equations. In this paper, we study the existence result of bounded solutions to a nonlinear anisotropic parabolic equations with degenerate coercivity, and the singular term in the right hand side. The model problem is \begin{equation*} \left\{\begin{array}{ll} \frac{\partial u}{\partial t}-\sum_{i=1}^{N}D_{i} \left(\frac{u^{p_{i}-1}(1+D u)^{-1}D u+\vert D u\vert^{p_{i}-2}D u}{(1+\vert u\vert)^{\theta}}\right)=\frac{f}{u^{\gamma}} & \hbox{in}\;\;Q, \\ u(x,0)=0 & \hbox{on}\;\; \Omega,\\ u =0 & \hbox{on}\;\; \Gamma, \end{array} \right. \end{equation*} where $\Omega$ is a bounded open subset of $\mathbb{R}^{N}$ $N\geq2$, $T>0$, $2\leq p_{i} \frac{N}{\overline{p}}+1$ ($\overline{p}$ defined in \eqref{0001}) and $Q=\Omega\times(0,T)$. The main idea in the proof is based on a Stampacchia's lemma with a good choice of test function that enables us to obtain a priori estimates. Mathematics Subject Classification (2010). 35K65; 35K55; 35B45; 35B65.

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Section: Introductionmentioning

confidence: 99%

Bounded Solutions for Anisotropic Degenerate Parabolic Problems with Singular Term

Zaater

Khelifi

2023

Preprint

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“…For constant-exponent cases (i.e., p(x) = p, r(x) = r and γ(x) = γ), the existence and regularity of solutions to problem (1) are studied in [1,3,7,8]. They proved that the solution is in W 1,q 0 (Ω) and u r+γ belongs to L 1 (Ω), where q = pr p+1−γ .…”

Section: Introduction Of Our Problemmentioning

confidence: 99%

Nonlinear elliptic equations with variable exponents involving singular nonlinearity

Khelifi¹,

Hadfi²

2021

Math. Model. Comput.

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“…In the same concept the authors in [23] proved the existence of solution to problem with 𝛾 > 0, f is a nonnegative function on , and is a nonnegative bounded Radon measures on . Hence Charkaoui and Alaa [7] established the existence of weak periodic solution to singular parabolic problems with 𝛾 > 0 and f is a nonnegative integrable function periodic in time with period T. Let us observe that we refer to [8,9,11,17,24] for more details on singular parabolic problems.…”

Section: Introductionmentioning

confidence: 99%

On nonlinear parabolic equations with singular lower order term

Hadfi

Ouardy

Ifzarne

et al. 2021

J Elliptic Parabol Equ

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In this paper we study existence and regularity results for solution to a nonlinear and singular parabolic problem. The model is where is a bounded open subset of ℝ N , N ≥ 2, Q is the cylinder × (0, T), T > 0, Γ the lateral surface × (0, T), q > 0, 𝛾 > 0, and f is non-negative function belonging to some Lebesgue space L m (Q), m ≥ 1 and u 0 ∈ L ∞ ( ) such that Keywords Singular problem • Nonlinear parabolic equations • Lower order term Mathematics Subject Classificationin , ∀ 𝜔 ⊂⊂ 𝛺, ∃ D 𝜔 > 0 ∶ u 0 ≥ D 𝜔 in 𝜔.

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Existence and regularity results for a singular parabolic equations with degenerate coercivity

Abstract: The aim of this paper is to prove existence and regularity of solutions for the following nonlinear singular parabolic problem    

Cited by 13 publications

References 22 publications

Bounded Solutions for Anisotropic Degenerate Parabolic Problems with Singular Term

Bounded Solutions for Anisotropic Degenerate Parabolic Problems with Singular Term

Nonlinear elliptic equations with variable exponents involving singular nonlinearity

On nonlinear parabolic equations with singular lower order term

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