Initial-Boundary Value Problems for Anisotropic Parabolic Equations with Variable Exponents of the Nonlinearity in Unbounded Domains with Conditions at Infinity
Анотація
We deal with the initial-boundary value problems with some restrictions at
infinity for linear and nonlinear anisotropic parabolic second-order equations in unbounded domains with respect to the spatial variables. The weak solutions of our problem in Lebesgue and Sobolev spaces with variable exponents is considered. We prove theorems on the existence and uniqueness of the weak solutions using the method based on Saint- Venant principle, and the monotonicity method. Moreover, we obtain estimate of the weak solutions.
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DOI: http://dx.doi.org/10.15421/142205
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