Supersolutions for a class of semilinear heat equations

作者：Robinson James C; Sierzega Mikolaj^*

来源：Revista Matematica Complutense, 2013, 26(2): 341-360.

DOI：10.1007/s13163-012-0108-9

• Nonlinear heat equation
• Reaction-diffusion equation
• Singular data
• Supersolutions
• Regularity
• Existence
• Global solutions

A semilinear heat equation with nonnegative measurable initial data is considered under the assumption that is nonnegative and nondecreasing and . A simple technique for proving existence and regularity based on the existence of supersolutions is presented, then a method of construction of local and global supersolutions is proposed. This approach is then applied to the model case with initial data in , for which an extension of the monotonicity-based existence argument is offered for the critical case () in all dimensions. New sufficient conditions for the existence of local and global classical solutions are derived in the critical and subcritical () range of parameters. Some possible generalisations of the method to a broader class of equations are discussed.

• 出版日期2013-7