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- W2072589636 abstract "This paper considers the global classical solvability (well-posedness) of a mixed initial-boundary value problem for semilinear hyperbolic systems with nonlinear reaction coupling of Lotka--Volterra type. The reaction nonlinearity is not globally Lipschitz in $L^2$ and has Lipschitz properties depending on an $L^infty$-norm bound. The well-posedness problem is reformulated in an abstract setting as a modified Cauchy problem with homogeneous boundary conditions and solved based on the Banach contraction mapping theorem. Extra regularity of the local solutions in Sobolev spaces is shown based on Moser-type inequalities. It is shown that global existence of classical solutions holds if a uniform a priori bound on the $L^infty$-norm of the solution and boundary term exists." @default.
- W2072589636 created "2016-06-24" @default.
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- W2072589636 date "2013-01-01" @default.
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- W2072589636 title "Classical Solutions in Sobolev Spaces for a Class of Hyperbolic Lotka--Volterra Systems" @default.
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- W2072589636 doi "https://doi.org/10.1137/090767303" @default.
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