Generalized Solutions of Semilinear Parabolic Equations

• Autores: Hideo Deguchi
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 146, Nº 4, 2005, págs. 279-294
• Idioma: inglés
• DOI: 10.1007/s00605-005-0311-6
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• Resumen

  • It is well-known that a semilinear parabolic equation has no unique solution in the classical sense. We study such equations from the viewpoint of generalized functions. By using approximations for generalized functions, we obtain results on existence and uniqueness of generalized solutions. Furthermore, we establish the relationship between generalized solutions and classical solutions