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- Title
On Blow-Up of Solutions of the Cauchy Problems for a Class of Nonlinear Equations of Ferrite Theory.
- Authors
Korpusov, M. O.; Shlyapugin, G. I.
- Abstract
In this paper, we consider three nonlinear equations of the theory of magnets with gradient nonlinearities ∇ u q , ∂ t ∇ u q , and ∂ t 2 ∇ u q are considered. For the corresponding Cauchy problems, we obtain results on local-in-time unique solvability in the weak sense and on blow-up for a finite time. These three equations have the same critical exponent q = 3/2 since weak solutions behave differently for 1 < q ≤ 3/2 and for q > 3/2. By the method of nonlinear capacity proposed by S. I. Pokhozhaev, we obtain a priori estimates, which imply the absence of local and global weak solutions.
- Subjects
NONLINEAR equations; FERRITES; NONLINEAR theories; CAUCHY problem; BLOWING up (Algebraic geometry); MAGNETS
- Publication
Journal of Mathematical Sciences, 2024, Vol 281, Issue 3, p418
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-024-07116-x