December 6, 2025Mathematical Methods in the Applied Sciences

Existence and Uniqueness of Mild Solutions of Viscous Burgers' Equation With Dirichlet Boundary Conditions

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Mild solutions exist for the viscous Burgers' equation under Dirichlet boundary conditions.
Using semigroup theory, the analysis confirms local-in-time solvability with a priori estimates.
Application of the Leray–Schauder topological degree establishes a fixed point associated with mild solutions.
The findings highlight the significance of compact and continuous mappings in functional analysis.

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Implication

This analysis demonstrates mild solutions in a Banach space for the viscous Burgers' equation, suggesting local solvability under minimal assumptions.

Cite This Study

M’hamed Elomari (2025) studied this question.

synapsesocial.com/papers/69337cdbb3f947a0a1259fa2 https://doi.org/10.1002/mma.70368

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Implication

This analysis demonstrates mild solutions in a Banach space for the viscous Burgers' equation, suggesting local solvability under minimal assumptions.

Existence and Uniqueness of Mild Solutions of Viscous Burgers' Equation With Dirichlet Boundary Conditions

Key Points

Discussion

Implication

Cite This Study

Existence and Uniqueness of Mild Solutions of Viscous Burgers' Equation With Dirichlet Boundary Conditions

Key Points

Discussion

Implication

Cite This Study

Also Consider

Also Consider