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• W3119378121 abstract "We study analytic smooth solutions of a general, strongly parabolic semilinear Cauchy problem of 2m-th order in (mathbb{R}^Ntimes (0,T)) with analytic coefficients (in space and time variables) and analytic initial data (in space variables).They are expressed in terms of holomorphic continuation of global (weak) solutions to the system valued in a suitable Besov interpolation space of (B^{s;p,p})-type at every time moment (tin [0,T]). Given (0 < T'< Tleq infty), it is proved that any (B^{s;p,p})-type solution (u: mathbb{R}^Ntimes (0,T)to mathbb{C}^M) with analytic initial data possesses a bounded holomorphic continuation (u(x + mathrm{i}y, sigma + mathrm{i}tau)) into a complex domain in (mathbb{C}^Ntimes mathbb{C}) defined by ((x,sigma)in mathbb{R}^Ntimes (T',T)), (|y| < A') and (|tau | < B'), where (A', B'> 0) are constants depending upon~(T'). The proof uses the extension of a weak solution to a (B^{s;p,p})-type solution in a domain in(mathbb{C}^Ntimes mathbb{C}), such that this extension satisfies the Cauchy-Riemann equations. The holomorphic extension is obtained with a help from holomorphic semigroups and maximal regularity theory for parabolic problems in Besov interpolation spaces of (B^{s;p,p})-type imbedded (densely and continuously) into an (L^p)-type Lebesgue space. Applications include emph{risk models} for European options in Mathematical Finance.&#x0D; For more information see https://ejde.math.txstate.edu/special/01/b1/abstr.html" @default.
• W3119378121 created "2021-01-18" @default.
• W3119378121 creator A5025788465 @default.
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• W3119378121 date "2021-10-06" @default.
• W3119378121 modified "2023-09-27" @default.
• W3119378121 title "Space-time analyticity of weak solutions to semilinear parabolic systems with variable coefficients" @default.
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• W3119378121 doi "https://doi.org/10.58997/ejde.sp.01.b1" @default.
• W3119378121 hasPublicationYear "2021" @default.
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