ABSTRACT
Let d ∈ {1, 2, 3, . . .} and Ω ⊂ ℝd be open bounded with Lipschitz boundary. Consider the reaction-diffusion parabolic problem
where T > 0, m ∈ [2, ∞), p ∈ (1, ∞) and
Funding statement: This research is funded by Vietnam National University Ho Chi Minh City (VNU-HCM) under grant number T2022-18-01.
REFERENCES
[1] Adams, R. A.—Fournier, J. J. F.: Sobolev Spaces, Academic Press, The Netherlands, 2003.Search in Google Scholar
[2] Bogelein, V.—Duzaar, F.—Marcellini, P.: Parabolic systems with p, q-growth: A variational approach, Arch. Ration. Mech. Anal. 210(1) (2013), 219–267.10.1007/s00205-013-0646-4Search in Google Scholar
[3] Balinsky, A. A.—Evans, W. D.—Lewis, R. T.: The Analysis and Geometry of Hardy’s Inequality. Universitext, Springer, Switzerland, 2015.10.1007/978-3-319-22870-9Search in Google Scholar
[4] Byun, S.-S.—Kim, W.: Global Calderon-Zygmund estimate for p-Laplacian parabolic system, Math. Ann. 383 (2022), 77–118.10.1007/s00208-020-02089-zSearch in Google Scholar
[5] Galaktonov, V. A.—Vazquez, J. L.: The problem of blow up in nonlinear parabolic equations, Discrete Contin. Dyn. Syst. 8(2) (2002), 399–433.10.3934/dcds.2002.8.399Search in Google Scholar
[6] Han, Y.: A new blow-up criterion for non-Newton filtration equations with special medium void, Rocky Mountain J. Math. 48(8) (2018), 2489–2501.10.1216/RMJ-2018-48-8-2489Search in Google Scholar
[7] Han, Y.: Blow-up phenomena for a reaction diffusion equation with special diffusion process, Appl. Anal. 101(6) (2022), 1971–1983.10.1080/00036811.2020.1792447Search in Google Scholar
[8] Han, Y.: Blow-up phenomena for a fourth-order parabolic equation with a general nonlinearity, J. Dyn. Control Syst. 27 (2021), 261–270.10.1007/s10883-020-09495-1Search in Google Scholar
[9] Hu, B.: Blow-up Theories for Semilinear Parabolic Equations. Lecture Notes in Math. 2018, Springer, Heidel-berg, 2011.10.1007/978-3-642-18460-4Search in Google Scholar
[10] Levine, H. A.: Some nonexistence and instability theorems for solutions of formally parabolic equation of the form Put = −Au + ℱu, Arch. Ration. Mech. Anal. 51 (1973), 371–386.10.1007/BF00263041Search in Google Scholar
[11] Philippin, G. A.: Blow-up phenomena for a class of fourth-order parabolic problems, Proc. Amer. Math. Soc. 143(6) (2015), 2507–2513.10.1090/S0002-9939-2015-12446-XSearch in Google Scholar
[12] Stein, E. M.: Singular Integrals and Differentiability Properties of Functions. Princeton Mathematical Series 30, Princeton University Press, Princeton, 1970.10.1515/9781400883882Search in Google Scholar
© 2023 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Parameters in Inversion Sequences
- On the Pecking Order Between Those of Mitsch and Clifford
- A Note on Cuts of Lattice-Valued Functions and Concept Lattices
- Trigonometric Sums and Riemann Zeta Function
- Notes on the Equation d(n) = d(φ(n)) and Related Inequalities
- Harmony of Asymmetric Variants of the Filbert and Lilbert Matrices in q-form
- Maximal Density and the Kappa Values for the Families {a, a + 1, 2a + 1, n} and {a, a + 1, 2a + 1, 3a + 1, n}
- Extensions in Time Scales Integral Inequalities of Jensen’s Type via Fink’s Identity
- A Note on Fractional Simpson Type Inequalities for Twice Differentiable Functions
- Extended Bromwich-Hansen Series
- Iterative Criteria for Oscillation of Third-Order Delay Differential Equations with p-Laplacian Operator
- Vallée-Poussin Theorem for Equations with Caputo Fractional Derivative
- On Oscillatory Behavior of Third Order Half-Linear Delay Differential Equations
- On Existence and Uniqueness of Solutions for Ordinary Differential Equations in Locally Convex Topological Linear Spaces
- Bounds on Blow-Up Time for a Higher-Order Non-Newtonian Filtration Equation
- On a Solvable System of Difference Equations in Terms of Generalized Fibonacci Numbers
- The Smallest and the Largest Families of Some Classes of 𝒜-Continuous Functions
- Type II Exponentiated Half-Logistic Gompertz-G Family of Distributions: Properties and Applications
- Strong Consistency of Least-Squares Estimators in the Simple Linear Errors-in-Variables Regression Model with Widely Orthant Dependent Random Variables
Articles in the same Issue
- Parameters in Inversion Sequences
- On the Pecking Order Between Those of Mitsch and Clifford
- A Note on Cuts of Lattice-Valued Functions and Concept Lattices
- Trigonometric Sums and Riemann Zeta Function
- Notes on the Equation d(n) = d(φ(n)) and Related Inequalities
- Harmony of Asymmetric Variants of the Filbert and Lilbert Matrices in q-form
- Maximal Density and the Kappa Values for the Families {a, a + 1, 2a + 1, n} and {a, a + 1, 2a + 1, 3a + 1, n}
- Extensions in Time Scales Integral Inequalities of Jensen’s Type via Fink’s Identity
- A Note on Fractional Simpson Type Inequalities for Twice Differentiable Functions
- Extended Bromwich-Hansen Series
- Iterative Criteria for Oscillation of Third-Order Delay Differential Equations with p-Laplacian Operator
- Vallée-Poussin Theorem for Equations with Caputo Fractional Derivative
- On Oscillatory Behavior of Third Order Half-Linear Delay Differential Equations
- On Existence and Uniqueness of Solutions for Ordinary Differential Equations in Locally Convex Topological Linear Spaces
- Bounds on Blow-Up Time for a Higher-Order Non-Newtonian Filtration Equation
- On a Solvable System of Difference Equations in Terms of Generalized Fibonacci Numbers
- The Smallest and the Largest Families of Some Classes of 𝒜-Continuous Functions
- Type II Exponentiated Half-Logistic Gompertz-G Family of Distributions: Properties and Applications
- Strong Consistency of Least-Squares Estimators in the Simple Linear Errors-in-Variables Regression Model with Widely Orthant Dependent Random Variables