| Summary: | The existence and uniqueness of entropy solutions for a class of parabolic equations involving a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Laplace operator are investigated. We first prove existence of the global weak solution for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Laplacian equations with regular initial data via the difference and variation methods as well as the standard domain expansion technique. Then, by constructing and solving a related approximation problem, the entropy solution for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Laplacian equations with irregular initial data in whole space is also obtained.
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