Fundamental Transformations to Inhomogeneous Parabolic PDEs

Sameerah Jamal

doi:10.1155/jom/5578333

January 1, 2025Journal of MathematicsOpen Access

Fundamental Transformations to Inhomogeneous Parabolic PDEs

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Key Points

Transformations can simplify inhomogeneous parabolic equations into a target equation with clear structure.
Key findings include a necessary condition that enables inhomogeneity to vanish in these equations.
The method of integrability is demonstrated through various examples, illustrating practical applications.
Understanding these transformations may lead to improvements in solving complex parabolic equations.

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Implication

This analysis reveals a necessary condition for vanishing inhomogeneity in parabolic equations, indicating novel mappings.

Abstract

The present paper is devoted to inhomogeneous (1 + 1) parabolic equations. In particular, we find a mapping which transforms the equations into a target equation. We prove a necessary condition which allows for the inhomogeneity to vanish. Consequently, we provide a concise presentation on a method of integrability of these equations. The theory is illustrated by several examples.

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Sameerah Jamal (2025) studied this question.

synapsesocial.com/papers/68c1c32754b1d3bfb60f0f50 https://doi.org/10.1155/jom/5578333

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Fundamental Transformations to Inhomogeneous Parabolic PDEs

Key Points

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Implication

Abstract

Discussion

Cite This Study

Fundamental Transformations to Inhomogeneous Parabolic PDEs

Key Points

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Implication

Abstract

Discussion

Cite This Study

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