Global existence for a semilinear prabolic Volterra equation.
Jan Prüss, Philippe Clément (1992)
Mathematische Zeitschrift
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Displaying similar documents to “The blow-up solutions of integral equations”
Global existence for a semilinear prabolic Volterra equation.
A Volterra inequality with the power type nonlinear kernel.
Mydlarczyk, W. (2001)
Journal of Inequalities and Applications [electronic only]
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Similarity stabilizes blow-up
Steve Schochet (1999)
Journées équations aux dérivées partielles
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The blow-up of solutions to a quasilinear heat equation is studied using a similarity transformation that turns the equation into a nonlocal equation whose steady solutions are stable. This allows energy methods to be used, instead of the comparison principles used previously. Among the questions discussed are the time and location of blow-up of perturbations of the steady blow-up profile.
An approximate solution of some Volterra integral equation with a smooth kernel
M. Niedziela (2008)
Applicationes Mathematicae
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The behaviour near the origin of nontrivial solutions to integral Volterra equations with a power nonlinearity is studied. Estimates of nontrivial solutions are given and some numerical examples are considered.
The problems of blow-up for nonlinear heat equations. Complete blow-up and avalanche formation
Juan Luis Vázquez (2004)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We review the main mathematical questions posed in blow-up problems for reaction-diffusion equations and discuss results of the author and collaborators on the subjects of continuation of solutions after blow-up, existence of transient blow-up solutions (so-called peaking solutions) and avalanche formation as a mechanism of complete blow-up.
Note on some integral Volterra equations.
W. Okrasinski (1993)
Extracta Mathematicae
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On blow-up at space infinity for semilinear heat equations
Giga, Y., Umeda, N.
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On a Staffans type inequality for vector Volterra integro-differential equations
G. Karakostas (1987)
Colloquium Mathematicae
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The existence of solutions to a Volterra integral equation
Wojciech Mydlarczyk (1996)
Annales Polonici Mathematici
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We study the equation u = k∗g(u) with k such that ln k is convex or concave and g is monotonic. Some necessary and sufficient conditions for the existence of nontrivial continuous solutions u of this equation are given.