Mykola Yaremenko, "Aspects of Solvability Theory for Quasilinear Parabolic Systems in Specific Form with the Singular Coefficients," Proof, vol. 3, pp. 8-13, 2023, DOI:10.37394/232020.2023.3.2
Mykola Yaremenko. Aspects of Solvability Theory for Quasilinear Parabolic Systems in Specific Form with the Singular Coefficients.
Proof. 2023;3:8-13. 10.37394/232020.2023.3.2
PROOF
Print ISSN: 2944-9162, E-ISSN: 2732-9941 An Open Access International Journal of Applied Science and Engineering
Volume 3, 2023
Aspects of Solvability Theory for Quasilinear Parabolic Systems in Specific Form with the Singular Coefficients
Author:
Abstract: In this paper, we study a quasilinear parabolic system in the form $$ θ_{t} \vec{u}= \nabla_{i}(a_{ij} (x, t, \vec{u}) \nabla_{j} \vec{u})+\vec{b}(x, t, \vec{u},\nabla\vec{u})$$, where $$ \vec{u}(x,t)$$ is an unknown N-dimensional vector over a domain $$D_{T}=Ωχ[0,T]$$, we assume the weak general conditions on the structural coefficients, demanding that the singular term satisfy the formboundary conditions.
Keywords:
Quasilinear Partial Differential Equation, Holder solution, regularity theory, form-bounded, Parabolic equation, Weak Solution, a Priori Estimation
Pages: 8-13 DOI: 10.37394/232020.2023.3.2WSEAS Transactions on Proof, ISSN / E-ISSN: 2944-9162 / 2732-9941, Volume 3, 2023, Art. #2
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