1. Large time behavior of reaction–diffusion equations with Bessel generators
- Author
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López-Mimbela, José Alfredo and Privault, Nicolas
- Subjects
- *
REACTION-diffusion equations , *PARTIAL differential equations , *EXPONENTS , *MATHEMATICAL formulas , *INITIAL value problems , *BLOWING up (Algebraic geometry) , *EXISTENCE theorems , *MATHEMATICAL constants - Abstract
Abstract: We investigate explosion in finite time of one-dimensional semilinear equations of the form with initial value , where is positive and , are constants. In the free case we provide conditions on φ under which any positive nontrivial solution is non-global. In the case and , , which includes in the special case the equation we use the Feynman–Kac formula for Bessel processes to give conditions on the equation parameters ensuring finite-time blowup and existence of nontrivial positive global solutions. [Copyright &y& Elsevier]
- Published
- 2011
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