Theoretical analysis demonstrates existence criteria for multiple nonnegative solutions in parabolic equations on time scales, suggesting broader applicability to models like Burgers' equation.
The class of parabolic equations in time sclases with forward jum operators are investigated for existence of at least one solution, at least two nonnegative and at least three nonnegative solutions. For this aim, a new integral representation of the solutions is derived. The results are illustrated by using the Burgers equation.
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Georgiev et al. (2026) studied this question.
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