Well-posedness for Hardy–Hénon parabolic equations with fractional Brownian noise
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Alòs, E., Mazet, O., Nualart, D.: Stochastic calculus with respectto Gaussian processes. Ann. Probab. 29, 766–801 (1999)
Ben Slimene, B., Tayachi, S., Weissler, F.B.: Well-posedness, global existence and large time behavior for Hardy–Hénon parabolic equations. Nonlinear Anal. 152, 116–148 (2017)
Bonaccorsi, S., Tudor, C.: Dissipative stochastic evolution equationsdriven by general Gaussian and non-Gaussian noise. J. Dyn. Differ. Equat. 23, 791–816 (2011)
Brezis, H., Casenave, T.: A nonlinear heat equation with singular initial data. Journ. d’anal. math 68, 73–90 (1996)
Brzezniak, Z., Neerven, J., Salopek, D.: Stochastic evolution equa-tions driven by Liouville fractional Brownian motion. Czechoslovak Math. J. 62, 1–27 (2012)
Clarke, J., Olivera, C.: Local $$L^p-$$ Solution for Semilinear Heat Equation with Fractional Noise. arXiv: 1902.06084
Coupek, P., Maslowski, B.: Stochastic evolution equations with Volterra noise. Stochast. Process. Appl. 127, 877–900 (2017)
Coupek, P., Maslowski, B., Ondrejat, M.: $$L^p-$$valued stochasticconvolution integral driven by Volterra noise. Stoch. Dyn. 18, 1850048 (2018)
Da Prato, G., Zabczyk, J.: Stochastic Equations in Infinite Dimensions, Encyclopedia of Mathematics and Its Applications, 44. Cambridge University Press, Cambridge (1992)
Duncan, T.E., Pasik-Duncan, B., Maslowski, B.: Fractional Brown-ian motion and stochastic equations in Hilbert spaces. Stoch. Dyn. 2, 225–250 (2002)
Galaktionov, V.A., Pohozaev, S.I.: Existence and blow-up for higher-order semilinear parabolic equations: majorizing order-preserving operators. Indiana Univ. Math. J. 51, 1321–1338 (2002)
Galaktionov, V.A., Pohozaev, S.I.: Blow-up and critical exponents for nonlinear hyperbolic equations. Nonlinear Anal. 53, 453–466 (2003)
Haraux, A., Weissler, F.B.: Non uniqueness for a semilinear initial value problem. Indiana Univ. Math. J. 31, 167–189 (1982)
Ibrahim, S., Jrad, R., Majdoub, M., Saanouni, T.: Local well posedness of a 2D semilinear heat equation. Bull. Belg. Math. Soc. Simon Stevin 21, 535–551 (2014)
Ioku, N.: The cauchy problem for heat equations with exponential nonlinearity. J. Differ. Equ. 251, 1172–1194 (2011)
Ioku, N., Ruf, B., Terraneo, E.: Existence, Non-existence, and Uniqueness for a Heat Equation with Exponential Nonlinearity in $${\mathbb{R}}^2$$. Math. Phys. Anal. Geom. 18, Art. 29, 19 (2015)
Kaplan, S.: On the growth of solutions of quasi-linear parabolic equations. Commun. Pure Appl. Math. 16, 305–330 (1963)
Kolmogorov, A.N.: Wienerische Spiralen und einige andere interessante Kurven im Hilbertschen Raum. C. R. (Doklady). Acad. URSS (N.S.) 26, 115–118 (1940)
Levine, H.A.: Some nonexistence and instability theorems for solutions of formally parabolic equations of the form $${\cal{P}}u_t=-{{\cal{A}}}u+{{\cal{F}}}(u)$$. Arch. Rational Mech. Anal. 51, 371–386 (1973)
Majdoub, M., Otsmane, S., Tayachi, S.: Local well-posedness and global existence for the Biharmonic heat equation with exponential nonlinearity. Adv. Differ. Equ. 23, 489–522 (2018)
Majdoub, M., Tayachi, S.: Well-posedness, global existence and decay estimates for the heat equation with general power-exponential nonlinearities. In: Proceedings of the International Congress on of Mathematics, Rio de Janeiro, 2, 2379–2404 (2018)
Majdoub, M., Tayachi, S.: Global existence and decay estimates for the heat equation with exponential nonlinearity. Funkcialaj Ekvacioj (To appear)
Maslowski, B., Schmalfuss, B.: Random dynamical systems and stationary solutions of differential equations driven by the fractional Brownian motion. Stoch. Anal. Appl. 22, 1577–1607 (2004)
Miao, C., Zhang, B.: The Cauchy problem for semilinear parabolic equations in Besov spaces. Houston J. Math. 30, 829–878 (2004)
Nualart, D.: The Malliavin calculus and related topics, 2nd Ed. Probability and Its Application (New York). Springer, Berlin (2006)
Pucci, P., Serrin, J.: Global nonexistence for abstract evolution equations with positive initial energy. J. Differ. Equ. 150, 203–214 (1998)
Quittner, P., Souplet, P.: Superlinear Parabolic Problems, xii+584. Birkhäuser Verlag, Basel (2007)
Ribaud, F.: Cauchy problem for semilinear parabolic equations with initial data in $$H^s_p({ R}^n)$$ spaces. Rev. Mat. Iberoamericana 14, 1–46 (1998)
Ruf, B., Terraneo, E.: The Cauchy problem for a semilinear heat equation with singular initial data, Evolution equations, semigroups and functional analysis (Milano, 2000). In: Programming Nonlinear Differential Equations Applications, 295–309. Birkhäuser, Basel (2002)
Sanz-Sole, M., Vuillermot, P.-A.: Mild solutions for a class of fractional SPDEs and their sample paths. J. Evol. Equ. 9, 235–265 (2009)
Tayachi, S.: Uniqueness and non-uniqueness of solutions for critical Hardy–Hénon parabolic equations. J. Math. Anal. Appl. 488, 123976 (2020)
Weissler, F.B.: Local existence and nonexistence for semilinear parabolic equations in $$L^{p}$$. Indiana Univ. Math. J. 29, 79–102 (1980)